Calculus Examples

$y = 5 x$ , $x = 5$ , $y = \frac{5}{x^{2}}$

Step 1

Solve by substitution to find the intersection between the curves.

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Step 1.1

Eliminate the equal sides of each equation and combine.

$5 x = \frac{5}{x^{2}}$

Step 1.2

Solve $5 x = \frac{5}{x^{2}}$ for $x$ .

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Step 1.2.1

Find the LCD of the terms in the equation.

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Step 1.2.1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, x^{2} + y = \frac{5}{x^{2}}$

Step 1.2.1.2

The LCM of one and any expression is the expression.

$x^{2} + y = \frac{5}{x^{2}}$

Step 1.2.2

Multiply each term in $5 x = \frac{5}{x^{2}}$ by $x^{2}$ to eliminate the fractions.

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Step 1.2.2.1

Multiply each term in $5 x = \frac{5}{x^{2}}$ by $x^{2}$ .

$5 x \cdot x^{2} = \frac{5}{x^{2}} x^{2}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 1.2.2.2.1.1

Move $x^{2}$ .

$5 (x^{2} x) = \frac{5}{x^{2}} x^{2}$

Step 1.2.2.2.1.2

Multiply $x^{2}$ by $x$ .

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Step 1.2.2.2.1.2.1

Raise $x$ to the power of $1$ .

$5 (x^{2} x^{1}) = \frac{5}{x^{2}} x^{2}$

Step 1.2.2.2.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 x^{2 + 1} = \frac{5}{x^{2}} x^{2}$

Step 1.2.2.2.1.3

Add $2$ and $1$ .

$5 x^{3} = \frac{5}{x^{2}} x^{2}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Cancel the common factor of $x^{2}$ .

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Step 1.2.2.3.1.1

Cancel the common factor.

$5 x^{3} = \frac{5}{x^{2}} x^{2}$

Step 1.2.2.3.1.2

Rewrite the expression.

$5 x^{3} = 5$

Step 1.2.3

Solve the equation.

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Step 1.2.3.1

Subtract $5$ from both sides of the equation.

$5 x^{3} - 5 = 0$

Step 1.2.3.2

Factor the left side of the equation.

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Step 1.2.3.2.1

Factor $5$ out of $5 x^{3} - 5$ .

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Step 1.2.3.2.1.1

Factor $5$ out of $5 x^{3}$ .

$5 (x^{3}) - 5 = 0$

Step 1.2.3.2.1.2

Factor $5$ out of $- 5$ .

$5 (x^{3}) + 5 (- 1) = 0$

Step 1.2.3.2.1.3

Factor $5$ out of $5 (x^{3}) + 5 (- 1)$ .

$5 (x^{3} - 1) = 0$

Step 1.2.3.2.2

Rewrite $1$ as $1^{3}$ .

$5 (x^{3} - 1^{3}) = 0$

Step 1.2.3.2.3

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 1$ .

$5 ((x - 1) (x^{2} + x \cdot 1 + 1^{2})) = 0$

Step 1.2.3.2.4

Factor.

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Step 1.2.3.2.4.1

Simplify.

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Step 1.2.3.2.4.1.1

Multiply $x$ by $1$ .

$5 ((x - 1) (x^{2} + x + 1^{2})) = 0$

Step 1.2.3.2.4.1.2

One to any power is one.

$5 ((x - 1) (x^{2} + x + 1)) = 0$

Step 1.2.3.2.4.2

Remove unnecessary parentheses.

$5 (x - 1) (x^{2} + x + 1) = 0$

Step 1.2.3.3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 1 = 0$

$x^{2} + x + 1 = 0 + y = \frac{5}{x^{2}}$

Step 1.2.3.4

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 1.2.3.4.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 1.2.3.4.2

Add $1$ to both sides of the equation.

$x = 1$

Step 1.2.3.5

Set $x^{2} + x + 1$ equal to $0$ and solve for $x$ .

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Step 1.2.3.5.1

Set $x^{2} + x + 1$ equal to $0$ .

$x^{2} + x + 1 = 0$

Step 1.2.3.5.2

Solve $x^{2} + x + 1 = 0$ for $x$ .

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Step 1.2.3.5.2.1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a} + y = \frac{5}{x^{2}}$

Step 1.2.3.5.2.2

Substitute the values $a = 1$ , $b = 1$ , and $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (1 \cdot 1)}}{2 \cdot 1} + y = \frac{5}{x^{2}}$

Step 1.2.3.5.2.3

Simplify.

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Step 1.2.3.5.2.3.1

Simplify the numerator.

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Step 1.2.3.5.2.3.1.1

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1 \cdot 1}}{2 \cdot 1}$

Step 1.2.3.5.2.3.1.2

Multiply $- 4 \cdot 1 \cdot 1$ .

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Step 1.2.3.5.2.3.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1}}{2 \cdot 1}$

Step 1.2.3.5.2.3.1.2.2

Multiply $- 4$ by $1$ .

$x = \frac{- 1 \pm \sqrt{1 - 4}}{2 \cdot 1}$

Step 1.2.3.5.2.3.1.3

Subtract $4$ from $1$ .

$x = \frac{- 1 \pm \sqrt{- 3}}{2 \cdot 1}$

Step 1.2.3.5.2.3.1.4

Rewrite $- 3$ as $- 1 (3)$ .

$x = \frac{- 1 \pm \sqrt{- 1 \cdot 3}}{2 \cdot 1}$

Step 1.2.3.5.2.3.1.5

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$x = \frac{- 1 \pm \sqrt{- 1} \cdot \sqrt{3}}{2 \cdot 1}$

Step 1.2.3.5.2.3.1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 1 \pm i \sqrt{3}}{2 \cdot 1}$

Step 1.2.3.5.2.3.2

Multiply $2$ by $1$ .

$x = \frac{- 1 \pm i \sqrt{3}}{2}$

Step 1.2.3.5.2.4

Simplify the expression to solve for the $+$ portion of the $\pm$ .

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Step 1.2.3.5.2.4.1

Simplify the numerator.

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Step 1.2.3.5.2.4.1.1

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1 \cdot 1}}{2 \cdot 1}$

Step 1.2.3.5.2.4.1.2

Multiply $- 4 \cdot 1 \cdot 1$ .

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Step 1.2.3.5.2.4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1}}{2 \cdot 1}$

Step 1.2.3.5.2.4.1.2.2

Multiply $- 4$ by $1$ .

$x = \frac{- 1 \pm \sqrt{1 - 4}}{2 \cdot 1}$

Step 1.2.3.5.2.4.1.3

Subtract $4$ from $1$ .

$x = \frac{- 1 \pm \sqrt{- 3}}{2 \cdot 1}$

Step 1.2.3.5.2.4.1.4

Rewrite $- 3$ as $- 1 (3)$ .

$x = \frac{- 1 \pm \sqrt{- 1 \cdot 3}}{2 \cdot 1}$

Step 1.2.3.5.2.4.1.5

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$x = \frac{- 1 \pm \sqrt{- 1} \cdot \sqrt{3}}{2 \cdot 1}$

Step 1.2.3.5.2.4.1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 1 \pm i \sqrt{3}}{2 \cdot 1}$

Step 1.2.3.5.2.4.2

Multiply $2$ by $1$ .

$x = \frac{- 1 \pm i \sqrt{3}}{2}$

Step 1.2.3.5.2.4.3

Change the $\pm$ to $+$ .

$x = \frac{- 1 + i \sqrt{3}}{2}$

Step 1.2.3.5.2.4.4

Rewrite $- 1$ as $- 1 (1)$ .

$x = \frac{- 1 \cdot 1 + i \sqrt{3}}{2}$

Step 1.2.3.5.2.4.5

Factor $- 1$ out of $i \sqrt{3}$ .

$x = \frac{- 1 \cdot 1 - (- i \sqrt{3})}{2}$

Step 1.2.3.5.2.4.6

Factor $- 1$ out of $- 1 (1) - (- i \sqrt{3})$ .

$x = \frac{- 1 (1 - i \sqrt{3})}{2}$

Step 1.2.3.5.2.4.7

Move the negative in front of the fraction.

$x = - \frac{1 - i \sqrt{3}}{2}$

Step 1.2.3.5.2.5

Simplify the expression to solve for the $-$ portion of the $\pm$ .

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Step 1.2.3.5.2.5.1

Simplify the numerator.

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Step 1.2.3.5.2.5.1.1

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1 \cdot 1}}{2 \cdot 1}$

Step 1.2.3.5.2.5.1.2

Multiply $- 4 \cdot 1 \cdot 1$ .

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Step 1.2.3.5.2.5.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1}}{2 \cdot 1}$

Step 1.2.3.5.2.5.1.2.2

Multiply $- 4$ by $1$ .

$x = \frac{- 1 \pm \sqrt{1 - 4}}{2 \cdot 1}$

Step 1.2.3.5.2.5.1.3

Subtract $4$ from $1$ .

$x = \frac{- 1 \pm \sqrt{- 3}}{2 \cdot 1}$

Step 1.2.3.5.2.5.1.4

Rewrite $- 3$ as $- 1 (3)$ .

$x = \frac{- 1 \pm \sqrt{- 1 \cdot 3}}{2 \cdot 1}$

Step 1.2.3.5.2.5.1.5

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$x = \frac{- 1 \pm \sqrt{- 1} \cdot \sqrt{3}}{2 \cdot 1}$

Step 1.2.3.5.2.5.1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 1 \pm i \sqrt{3}}{2 \cdot 1}$

Step 1.2.3.5.2.5.2

Multiply $2$ by $1$ .

$x = \frac{- 1 \pm i \sqrt{3}}{2}$

Step 1.2.3.5.2.5.3

Change the $\pm$ to $-$ .

$x = \frac{- 1 - i \sqrt{3}}{2}$

Step 1.2.3.5.2.5.4

Rewrite $- 1$ as $- 1 (1)$ .

$x = \frac{- 1 \cdot 1 - i \sqrt{3}}{2}$

Step 1.2.3.5.2.5.5

Factor $- 1$ out of $- i \sqrt{3}$ .

$x = \frac{- 1 \cdot 1 - (i \sqrt{3})}{2}$

Step 1.2.3.5.2.5.6

Factor $- 1$ out of $- 1 (1) - (i \sqrt{3})$ .

$x = \frac{- 1 (1 + i \sqrt{3})}{2}$

Step 1.2.3.5.2.5.7

Move the negative in front of the fraction.

$x = - \frac{1 + i \sqrt{3}}{2}$

Step 1.2.3.5.2.6

The final answer is the combination of both solutions.

$x = - \frac{1 - i \sqrt{3}}{2}, - \frac{1 + i \sqrt{3}}{2}$

Step 1.2.3.6

The final solution is all the values that make $5 (x - 1) (x^{2} + x + 1) = 0$ true.

$x = 1, - \frac{1 - i \sqrt{3}}{2}, - \frac{1 + i \sqrt{3}}{2}$

Step 1.3

Evaluate $y$ when $x = 1$ .

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Step 1.3.1

Substitute $1$ for $x$ .

$y = \frac{5}{{(1)}^{2}}$

Step 1.3.2

Substitute $1$ for $x$ in $y = \frac{5}{{(1)}^{2}}$ and solve for $y$ .

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Step 1.3.2.1

Remove parentheses.

$y = \frac{5}{1^{2}}$

Step 1.3.2.2

Simplify $\frac{5}{1^{2}}$ .

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Step 1.3.2.2.1

One to any power is one.

$y = \frac{5}{1}$

Step 1.3.2.2.2

Divide $5$ by $1$ .

$y = 5$

Step 1.4

Evaluate $y$ when $x = - \frac{1 - i \sqrt{3}}{2}$ .

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Step 1.4.1

Substitute $- \frac{1 - i \sqrt{3}}{2}$ for $x$ .

$y = \frac{5}{{(- \frac{1 - i \sqrt{3}}{2})}^{2}}$

Step 1.4.2

Simplify $\frac{5}{{(- \frac{1 - i \sqrt{3}}{2})}^{2}}$ .

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Step 1.4.2.1

Simplify the denominator.

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Step 1.4.2.1.1

Apply the product rule to $- \frac{1 - i \sqrt{3}}{2}$ .

$y = \frac{5}{{(- 1)}^{2} {(\frac{1 - i \sqrt{3}}{2})}^{2}}$

Step 1.4.2.1.2

Raise $- 1$ to the power of $2$ .

$y = \frac{5}{1 {(\frac{1 - i \sqrt{3}}{2})}^{2}}$

Step 1.4.2.1.3

Apply the product rule to $\frac{1 - i \sqrt{3}}{2}$ .

$y = \frac{5}{1 \frac{{(1 - i \sqrt{3})}^{2}}{2^{2}}}$

Step 1.4.2.1.4

Raise $2$ to the power of $2$ .

$y = \frac{5}{1 \frac{{(1 - i \sqrt{3})}^{2}}{4}}$

Step 1.4.2.1.5

Rewrite ${(1 - i \sqrt{3})}^{2}$ as $(1 - i \sqrt{3}) (1 - i \sqrt{3})$ .

$y = \frac{5}{1 \frac{(1 - i \sqrt{3}) (1 - i \sqrt{3})}{4}}$

Step 1.4.2.1.6

Expand $(1 - i \sqrt{3}) (1 - i \sqrt{3})$ using the FOIL Method.

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Step 1.4.2.1.6.1

Apply the distributive property.

$y = \frac{5}{1 \frac{1 (1 - i \sqrt{3}) - i \sqrt{3} (1 - i \sqrt{3})}{4}}$

Step 1.4.2.1.6.2

Apply the distributive property.

$y = \frac{5}{1 \frac{1 \cdot 1 + 1 (- i \sqrt{3}) - i \sqrt{3} (1 - i \sqrt{3})}{4}}$

Step 1.4.2.1.6.3

Apply the distributive property.

$y = \frac{5}{1 \frac{1 \cdot 1 + 1 (- i \sqrt{3}) - i \sqrt{3} \cdot 1 - i \sqrt{3} (- i \sqrt{3})}{4}}$

Step 1.4.2.1.7

Simplify and combine like terms.

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Step 1.4.2.1.7.1

Simplify each term.

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Step 1.4.2.1.7.1.1

Multiply $1$ by $1$ .

$y = \frac{5}{1 \frac{1 + 1 (- i \sqrt{3}) - i \sqrt{3} \cdot 1 - i \sqrt{3} (- i \sqrt{3})}{4}}$

Step 1.4.2.1.7.1.2

Multiply $- i \sqrt{3}$ by $1$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} \cdot 1 - i \sqrt{3} (- i \sqrt{3})}{4}}$

Step 1.4.2.1.7.1.3

Multiply $- 1$ by $1$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} - i \sqrt{3} (- i \sqrt{3})}{4}}$

Step 1.4.2.1.7.1.4

Multiply $- i \sqrt{3} (- i \sqrt{3})$ .

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Step 1.4.2.1.7.1.4.1

Multiply $- 1$ by $- 1$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + 1 i \sqrt{3} (i \sqrt{3})}{4}}$

Step 1.4.2.1.7.1.4.2

Multiply $\sqrt{3}$ by $1$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + \sqrt{3} i (i \sqrt{3})}{4}}$

Step 1.4.2.1.7.1.4.3

Raise $\sqrt{3}$ to the power of $1$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + {\sqrt{3}}^{1} \sqrt{3} i i}{4}}$

Step 1.4.2.1.7.1.4.4

Raise $\sqrt{3}$ to the power of $1$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + {\sqrt{3}}^{1} {\sqrt{3}}^{1} i i}{4}}$

Step 1.4.2.1.7.1.4.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + {\sqrt{3}}^{1 + 1} i i}{4}}$

Step 1.4.2.1.7.1.4.6

Add $1$ and $1$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + {\sqrt{3}}^{2} i i}{4}}$

Step 1.4.2.1.7.1.4.7

Raise $i$ to the power of $1$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + {\sqrt{3}}^{2} (i^{1} i)}{4}}$

Step 1.4.2.1.7.1.4.8

Raise $i$ to the power of $1$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + {\sqrt{3}}^{2} (i^{1} i^{1})}{4}}$

Step 1.4.2.1.7.1.4.9

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + {\sqrt{3}}^{2} i^{1 + 1}}{4}}$

Step 1.4.2.1.7.1.4.10

Add $1$ and $1$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + {\sqrt{3}}^{2} i^{2}}{4}}$

Step 1.4.2.1.7.1.5

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 1.4.2.1.7.1.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + {(3^{\frac{1}{2}})}^{2} i^{2}}{4}}$

Step 1.4.2.1.7.1.5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + 3^{\frac{1}{2} \cdot 2} i^{2}}{4}}$

Step 1.4.2.1.7.1.5.3

Combine $\frac{1}{2}$ and $2$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + 3^{\frac{2}{2}} i^{2}}{4}}$

Step 1.4.2.1.7.1.5.4

Cancel the common factor of $2$ .

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Step 1.4.2.1.7.1.5.4.1

Cancel the common factor.

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + 3^{\frac{2}{2}} i^{2}}{4}}$

Step 1.4.2.1.7.1.5.4.2

Rewrite the expression.

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + 3^{1} i^{2}}{4}}$

Step 1.4.2.1.7.1.5.5

Evaluate the exponent.

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + 3 i^{2}}{4}}$

Step 1.4.2.1.7.1.6

Rewrite $i^{2}$ as $- 1$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} + 3 \cdot - 1}{4}}$

Step 1.4.2.1.7.1.7

Multiply $3$ by $- 1$ .

$y = \frac{5}{1 \frac{1 - i \sqrt{3} - i \sqrt{3} - 3}{4}}$

Step 1.4.2.1.7.2

Subtract $3$ from $1$ .

$y = \frac{5}{1 \frac{- i \sqrt{3} - i \sqrt{3} - 2}{4}}$

Step 1.4.2.1.7.3

Subtract $i \sqrt{3}$ from $- i \sqrt{3}$ .

$y = \frac{5}{1 \frac{- 2 i \sqrt{3} - 2}{4}}$

Step 1.4.2.1.8

Reorder $- 2 i \sqrt{3}$ and $- 2$ .

$y = \frac{5}{1 \frac{- 2 - 2 i \sqrt{3}}{4}}$

Step 1.4.2.1.9

Cancel the common factor of $- 2 - 2 i \sqrt{3}$ and $4$ .

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Step 1.4.2.1.9.1

Factor $2$ out of $- 2$ .

$y = \frac{5}{1 \frac{2 (- 1) - 2 i \sqrt{3}}{4}}$

Step 1.4.2.1.9.2

Factor $2$ out of $- 2 i \sqrt{3}$ .

$y = \frac{5}{1 \frac{2 (- 1) + 2 (- i \sqrt{3})}{4}}$

Step 1.4.2.1.9.3

Factor $2$ out of $2 (- 1) + 2 (- i \sqrt{3})$ .

$y = \frac{5}{1 \frac{2 (- 1 - i \sqrt{3})}{4}}$

Step 1.4.2.1.9.4

Cancel the common factors.

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Step 1.4.2.1.9.4.1

Factor $2$ out of $4$ .

$y = \frac{5}{1 \frac{2 (- 1 - i \sqrt{3})}{2 \cdot 2}}$

Step 1.4.2.1.9.4.2

Cancel the common factor.

$y = \frac{5}{1 \frac{2 (- 1 - i \sqrt{3})}{2 \cdot 2}}$

Step 1.4.2.1.9.4.3

Rewrite the expression.

$y = \frac{5}{1 \frac{- 1 - i \sqrt{3}}{2}}$

Step 1.4.2.1.10

Multiply $\frac{- 1 - i \sqrt{3}}{2}$ by $1$ .

$y = \frac{5}{\frac{- 1 - i \sqrt{3}}{2}}$

Step 1.4.2.2

Multiply the numerator by the reciprocal of the denominator.

$y = 5 \frac{2}{- 1 - i \sqrt{3}}$

Step 1.4.2.3

Multiply the numerator and denominator of $\frac{2}{- 1 - 1.7320508 i}$ by the conjugate of $- 1 - 1.7320508 i$ to make the denominator real.

$y = 5 (\frac{2}{- 1 - 1.7320508 i} \cdot \frac{- 1 + 1.7320508 i}{- 1 + 1.7320508 i})$

Step 1.4.2.4

Multiply.

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Step 1.4.2.4.1

Combine.

$y = 5 \frac{2 (- 1 + 1.7320508 i)}{(- 1 - 1.7320508 i) (- 1 + 1.7320508 i)}$

Step 1.4.2.4.2

Simplify the numerator.

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Step 1.4.2.4.2.1

Apply the distributive property.

$y = 5 \frac{2 \cdot - 1 + 2 (1.7320508 i)}{(- 1 - 1.7320508 i) (- 1 + 1.7320508 i)}$

Step 1.4.2.4.2.2

Multiply $2$ by $- 1$ .

$y = 5 \frac{- 2 + 2 (1.7320508 i)}{(- 1 - 1.7320508 i) (- 1 + 1.7320508 i)}$

Step 1.4.2.4.2.3

Multiply $1.7320508$ by $2$ .

$y = 5 \frac{- 2 + 3.46410161 i}{(- 1 - 1.7320508 i) (- 1 + 1.7320508 i)}$

Step 1.4.2.4.3

Simplify the denominator.

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Step 1.4.2.4.3.1

Expand $(- 1 - 1.7320508 i) (- 1 + 1.7320508 i)$ using the FOIL Method.

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Step 1.4.2.4.3.1.1

Apply the distributive property.

$y = 5 \frac{- 2 + 3.46410161 i}{- 1 (- 1 + 1.7320508 i) - 1.7320508 i (- 1 + 1.7320508 i)}$

Step 1.4.2.4.3.1.2

Apply the distributive property.

$y = 5 \frac{- 2 + 3.46410161 i}{- 1 \cdot - 1 - 1 (1.7320508 i) - 1.7320508 i (- 1 + 1.7320508 i)}$

Step 1.4.2.4.3.1.3

Apply the distributive property.

$y = 5 \frac{- 2 + 3.46410161 i}{- 1 \cdot - 1 - 1 (1.7320508 i) - 1.7320508 i \cdot - 1 - 1.7320508 i (1.7320508 i)}$

Step 1.4.2.4.3.2

Simplify.

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Step 1.4.2.4.3.2.1

Multiply $- 1$ by $- 1$ .

$y = 5 \frac{- 2 + 3.46410161 i}{1 - 1 (1.7320508 i) - 1.7320508 i \cdot - 1 - 1.7320508 i (1.7320508 i)}$

Step 1.4.2.4.3.2.2

Multiply $1.7320508$ by $- 1$ .

$y = 5 \frac{- 2 + 3.46410161 i}{1 - 1.7320508 i - 1.7320508 i \cdot - 1 - 1.7320508 i (1.7320508 i)}$

Step 1.4.2.4.3.2.3

Multiply $- 1$ by $- 1.7320508$ .

$y = 5 \frac{- 2 + 3.46410161 i}{1 - 1.7320508 i + 1.7320508 i - 1.7320508 i (1.7320508 i)}$

Step 1.4.2.4.3.2.4

Multiply $1.7320508$ by $- 1.7320508$ .

$y = 5 \frac{- 2 + 3.46410161 i}{1 - 1.7320508 i + 1.7320508 i - 3 i i}$

Step 1.4.2.4.3.2.5

Raise $i$ to the power of $1$ .

$y = 5 \frac{- 2 + 3.46410161 i}{1 - 1.7320508 i + 1.7320508 i - 3 (i^{1} i)}$

Step 1.4.2.4.3.2.6

Raise $i$ to the power of $1$ .

$y = 5 \frac{- 2 + 3.46410161 i}{1 - 1.7320508 i + 1.7320508 i - 3 (i^{1} i^{1})}$

Step 1.4.2.4.3.2.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = 5 \frac{- 2 + 3.46410161 i}{1 - 1.7320508 i + 1.7320508 i - 3 i^{1 + 1}}$

Step 1.4.2.4.3.2.8

Add $1$ and $1$ .

$y = 5 \frac{- 2 + 3.46410161 i}{1 - 1.7320508 i + 1.7320508 i - 3 i^{2}}$

Step 1.4.2.4.3.2.9

Add $- 1.7320508 i$ and $1.7320508 i$ .

$y = 5 \frac{- 2 + 3.46410161 i}{1 + 0 i - 3 i^{2}}$

Step 1.4.2.4.3.3

Simplify each term.

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Step 1.4.2.4.3.3.1

Multiply $0$ by $i$ .

$y = 5 \frac{- 2 + 3.46410161 i}{1 + 0 - 3 i^{2}}$

Step 1.4.2.4.3.3.2

Rewrite $i^{2}$ as $- 1$ .

$y = 5 \frac{- 2 + 3.46410161 i}{1 + 0 - 3 \cdot - 1}$

Step 1.4.2.4.3.3.3

Multiply $- 3$ by $- 1$ .

$y = 5 \frac{- 2 + 3.46410161 i}{1 + 0 + 3}$

Step 1.4.2.4.3.4

Add $1$ and $0$ .

$y = 5 \frac{- 2 + 3.46410161 i}{1 + 3}$

Step 1.4.2.4.3.5

Add $1$ and $3$ .

$y = 5 \frac{- 2 + 3.46410161 i}{4}$

Step 1.4.2.5

Rewrite $- 2$ as $1 (- 2)$ .

$y = 5 \frac{1 (- 2) + 3.46410161 i}{4}$

Step 1.4.2.6

Factor $1$ out of $3.46410161 i$ .

$y = 5 \frac{1 (- 2) + 1 (3.46410161 i)}{4}$

Step 1.4.2.7

Factor $1$ out of $1 (- 2) + 1 (3.46410161 i)$ .

$y = 5 \frac{1 (- 2 + 3.46410161 i)}{4}$

Step 1.4.2.8

Factor $4$ out of $4$ .

$y = 5 \frac{1 (- 2 + 3.46410161 i)}{4 (1)}$

Step 1.4.2.9

Separate fractions.

$y = 5 (\frac{1}{4} \cdot \frac{- 2 + 3.46410161 i}{1})$

Step 1.4.2.10

Simplify the expression.

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Step 1.4.2.10.1

Divide $1$ by $4$ .

$y = 5 (0.25 \frac{- 2 + 3.46410161 i}{1})$

Step 1.4.2.10.2

Divide $- 2 + 3.46410161 i$ by $1$ .

$y = 5 (0.25 (- 2 + 3.46410161 i))$

Step 1.4.2.11

Apply the distributive property.

$y = 5 (0.25 \cdot - 2 + 0.25 (3.46410161 i))$

Step 1.4.2.12

Multiply.

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Step 1.4.2.12.1

Multiply $0.25$ by $- 2$ .

$y = 5 (- 0.5 + 0.25 (3.46410161 i))$

Step 1.4.2.12.2

Multiply $3.46410161$ by $0.25$ .

$y = 5 (- 0.5 + 0.8660254 i)$

Step 1.4.2.13

Apply the distributive property.

$y = 5 \cdot - 0.5 + 5 (0.8660254 i)$

Step 1.4.2.14

Multiply.

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Step 1.4.2.14.1

Multiply $5$ by $- 0.5$ .

$y = - 2.5 + 5 (0.8660254 i)$

Step 1.4.2.14.2

Multiply $0.8660254$ by $5$ .

$y = - 2.5 + 4.33012701 i$

Step 1.5

Evaluate $y$ when $x = - \frac{1 + i \sqrt{3}}{2}$ .

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Step 1.5.1

Substitute $- \frac{1 + i \sqrt{3}}{2}$ for $x$ .

$y = \frac{5}{{(- \frac{1 + i \sqrt{3}}{2})}^{2}}$

Step 1.5.2

Simplify $\frac{5}{{(- \frac{1 + i \sqrt{3}}{2})}^{2}}$ .

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Step 1.5.2.1

Simplify the denominator.

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Step 1.5.2.1.1

Apply the product rule to $- \frac{1 + i \sqrt{3}}{2}$ .

$y = \frac{5}{{(- 1)}^{2} {(\frac{1 + i \sqrt{3}}{2})}^{2}}$

Step 1.5.2.1.2

Raise $- 1$ to the power of $2$ .

$y = \frac{5}{1 {(\frac{1 + i \sqrt{3}}{2})}^{2}}$

Step 1.5.2.1.3

Apply the product rule to $\frac{1 + i \sqrt{3}}{2}$ .

$y = \frac{5}{1 \frac{{(1 + i \sqrt{3})}^{2}}{2^{2}}}$

Step 1.5.2.1.4

Raise $2$ to the power of $2$ .

$y = \frac{5}{1 \frac{{(1 + i \sqrt{3})}^{2}}{4}}$

Step 1.5.2.1.5

Rewrite ${(1 + i \sqrt{3})}^{2}$ as $(1 + i \sqrt{3}) (1 + i \sqrt{3})$ .

$y = \frac{5}{1 \frac{(1 + i \sqrt{3}) (1 + i \sqrt{3})}{4}}$

Step 1.5.2.1.6

Expand $(1 + i \sqrt{3}) (1 + i \sqrt{3})$ using the FOIL Method.

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Step 1.5.2.1.6.1

Apply the distributive property.

$y = \frac{5}{1 \frac{1 (1 + i \sqrt{3}) + i \sqrt{3} (1 + i \sqrt{3})}{4}}$

Step 1.5.2.1.6.2

Apply the distributive property.

$y = \frac{5}{1 \frac{1 \cdot 1 + 1 (i \sqrt{3}) + i \sqrt{3} (1 + i \sqrt{3})}{4}}$

Step 1.5.2.1.6.3

Apply the distributive property.

$y = \frac{5}{1 \frac{1 \cdot 1 + 1 (i \sqrt{3}) + i \sqrt{3} \cdot 1 + i \sqrt{3} (i \sqrt{3})}{4}}$

Step 1.5.2.1.7

Simplify and combine like terms.

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Step 1.5.2.1.7.1

Simplify each term.

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Step 1.5.2.1.7.1.1

Multiply $1$ by $1$ .

$y = \frac{5}{1 \frac{1 + 1 (i \sqrt{3}) + i \sqrt{3} \cdot 1 + i \sqrt{3} (i \sqrt{3})}{4}}$

Step 1.5.2.1.7.1.2

Multiply $i \sqrt{3}$ by $1$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} \cdot 1 + i \sqrt{3} (i \sqrt{3})}{4}}$

Step 1.5.2.1.7.1.3

Multiply $i$ by $1$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} + i \sqrt{3} (i \sqrt{3})}{4}}$

Step 1.5.2.1.7.1.4

Multiply $i \sqrt{3} (i \sqrt{3})$ .

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Step 1.5.2.1.7.1.4.1

Raise $i$ to the power of $1$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} + i^{1} i \sqrt{3} \sqrt{3}}{4}}$

Step 1.5.2.1.7.1.4.2

Raise $i$ to the power of $1$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} + i^{1} i^{1} \sqrt{3} \sqrt{3}}{4}}$

Step 1.5.2.1.7.1.4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} + i^{1 + 1} \sqrt{3} \sqrt{3}}{4}}$

Step 1.5.2.1.7.1.4.4

Add $1$ and $1$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} + i^{2} \sqrt{3} \sqrt{3}}{4}}$

Step 1.5.2.1.7.1.4.5

Raise $\sqrt{3}$ to the power of $1$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} + i^{2} ({\sqrt{3}}^{1} \sqrt{3})}{4}}$

Step 1.5.2.1.7.1.4.6

Raise $\sqrt{3}$ to the power of $1$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} + i^{2} ({\sqrt{3}}^{1} {\sqrt{3}}^{1})}{4}}$

Step 1.5.2.1.7.1.4.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} + i^{2} {\sqrt{3}}^{1 + 1}}{4}}$

Step 1.5.2.1.7.1.4.8

Add $1$ and $1$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} + i^{2} {\sqrt{3}}^{2}}{4}}$

Step 1.5.2.1.7.1.5

Rewrite $i^{2}$ as $- 1$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} - 1 {\sqrt{3}}^{2}}{4}}$

Step 1.5.2.1.7.1.6

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 1.5.2.1.7.1.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} - 1 {(3^{\frac{1}{2}})}^{2}}{4}}$

Step 1.5.2.1.7.1.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} - 1 \cdot 3^{\frac{1}{2} \cdot 2}}{4}}$

Step 1.5.2.1.7.1.6.3

Combine $\frac{1}{2}$ and $2$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} - 1 \cdot 3^{\frac{2}{2}}}{4}}$

Step 1.5.2.1.7.1.6.4

Cancel the common factor of $2$ .

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Step 1.5.2.1.7.1.6.4.1

Cancel the common factor.

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} - 1 \cdot 3^{\frac{2}{2}}}{4}}$

Step 1.5.2.1.7.1.6.4.2

Rewrite the expression.

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} - 1 \cdot 3^{1}}{4}}$

Step 1.5.2.1.7.1.6.5

Evaluate the exponent.

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} - 1 \cdot 3}{4}}$

Step 1.5.2.1.7.1.7

Multiply $- 1$ by $3$ .

$y = \frac{5}{1 \frac{1 + i \sqrt{3} + i \sqrt{3} - 3}{4}}$

Step 1.5.2.1.7.2

Subtract $3$ from $1$ .

$y = \frac{5}{1 \frac{i \sqrt{3} + i \sqrt{3} - 2}{4}}$

Step 1.5.2.1.7.3

Add $i \sqrt{3}$ and $i \sqrt{3}$ .

$y = \frac{5}{1 \frac{2 i \sqrt{3} - 2}{4}}$

Step 1.5.2.1.8

Reorder $2 i \sqrt{3}$ and $- 2$ .

$y = \frac{5}{1 \frac{- 2 + 2 i \sqrt{3}}{4}}$

Step 1.5.2.1.9

Cancel the common factor of $- 2 + 2 i \sqrt{3}$ and $4$ .

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Step 1.5.2.1.9.1

Factor $2$ out of $- 2$ .

$y = \frac{5}{1 \frac{2 \cdot - 1 + 2 i \sqrt{3}}{4}}$

Step 1.5.2.1.9.2

Factor $2$ out of $2 i \sqrt{3}$ .

$y = \frac{5}{1 \frac{2 \cdot - 1 + 2 (i \sqrt{3})}{4}}$

Step 1.5.2.1.9.3

Factor $2$ out of $2 \cdot - 1 + 2 (i \sqrt{3})$ .

$y = \frac{5}{1 \frac{2 \cdot (- 1 + i \sqrt{3})}{4}}$

Step 1.5.2.1.9.4

Cancel the common factors.

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Step 1.5.2.1.9.4.1

Factor $2$ out of $4$ .

$y = \frac{5}{1 \frac{2 \cdot (- 1 + i \sqrt{3})}{2 (2)}}$

Step 1.5.2.1.9.4.2

Cancel the common factor.

$y = \frac{5}{1 \frac{2 \cdot (- 1 + i \sqrt{3})}{2 \cdot 2}}$

Step 1.5.2.1.9.4.3

Rewrite the expression.

$y = \frac{5}{1 \frac{- 1 + i \sqrt{3}}{2}}$

Step 1.5.2.1.10

Multiply $\frac{- 1 + i \sqrt{3}}{2}$ by $1$ .

$y = \frac{5}{\frac{- 1 + i \sqrt{3}}{2}}$

Step 1.5.2.2

Multiply the numerator by the reciprocal of the denominator.

$y = 5 \frac{2}{- 1 + i \sqrt{3}}$

Step 1.5.2.3

Multiply the numerator and denominator of $\frac{2}{- 1 + 1.7320508 i}$ by the conjugate of $- 1 + 1.7320508 i$ to make the denominator real.

$y = 5 (\frac{2}{- 1 + 1.7320508 i} \cdot \frac{- 1 - 1.7320508 i}{- 1 - 1.7320508 i})$

Step 1.5.2.4

Multiply.

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Step 1.5.2.4.1

Combine.

$y = 5 \frac{2 (- 1 - 1.7320508 i)}{(- 1 + 1.7320508 i) (- 1 - 1.7320508 i)}$

Step 1.5.2.4.2

Simplify the numerator.

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Step 1.5.2.4.2.1

Apply the distributive property.

$y = 5 \frac{2 \cdot - 1 + 2 (- 1.7320508 i)}{(- 1 + 1.7320508 i) (- 1 - 1.7320508 i)}$

Step 1.5.2.4.2.2

Multiply $2$ by $- 1$ .

$y = 5 \frac{- 2 + 2 (- 1.7320508 i)}{(- 1 + 1.7320508 i) (- 1 - 1.7320508 i)}$

Step 1.5.2.4.2.3

Multiply $- 1.7320508$ by $2$ .

$y = 5 \frac{- 2 - 3.46410161 i}{(- 1 + 1.7320508 i) (- 1 - 1.7320508 i)}$

Step 1.5.2.4.3

Simplify the denominator.

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Step 1.5.2.4.3.1

Expand $(- 1 + 1.7320508 i) (- 1 - 1.7320508 i)$ using the FOIL Method.

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Step 1.5.2.4.3.1.1

Apply the distributive property.

$y = 5 \frac{- 2 - 3.46410161 i}{- 1 (- 1 - 1.7320508 i) + 1.7320508 i (- 1 - 1.7320508 i)}$

Step 1.5.2.4.3.1.2

Apply the distributive property.

$y = 5 \frac{- 2 - 3.46410161 i}{- 1 \cdot - 1 - 1 (- 1.7320508 i) + 1.7320508 i (- 1 - 1.7320508 i)}$

Step 1.5.2.4.3.1.3

Apply the distributive property.

$y = 5 \frac{- 2 - 3.46410161 i}{- 1 \cdot - 1 - 1 (- 1.7320508 i) + 1.7320508 i \cdot - 1 + 1.7320508 i (- 1.7320508 i)}$

Step 1.5.2.4.3.2

Simplify.

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Step 1.5.2.4.3.2.1

Multiply $- 1$ by $- 1$ .

$y = 5 \frac{- 2 - 3.46410161 i}{1 - 1 (- 1.7320508 i) + 1.7320508 i \cdot - 1 + 1.7320508 i (- 1.7320508 i)}$

Step 1.5.2.4.3.2.2

Multiply $- 1.7320508$ by $- 1$ .

$y = 5 \frac{- 2 - 3.46410161 i}{1 + 1.7320508 i + 1.7320508 i \cdot - 1 + 1.7320508 i (- 1.7320508 i)}$

Step 1.5.2.4.3.2.3

Multiply $- 1$ by $1.7320508$ .

$y = 5 \frac{- 2 - 3.46410161 i}{1 + 1.7320508 i - 1.7320508 i + 1.7320508 i (- 1.7320508 i)}$

Step 1.5.2.4.3.2.4

Multiply $- 1.7320508$ by $1.7320508$ .

$y = 5 \frac{- 2 - 3.46410161 i}{1 + 1.7320508 i - 1.7320508 i - 3 i i}$

Step 1.5.2.4.3.2.5

Raise $i$ to the power of $1$ .

$y = 5 \frac{- 2 - 3.46410161 i}{1 + 1.7320508 i - 1.7320508 i - 3 (i^{1} i)}$

Step 1.5.2.4.3.2.6

Raise $i$ to the power of $1$ .

$y = 5 \frac{- 2 - 3.46410161 i}{1 + 1.7320508 i - 1.7320508 i - 3 (i^{1} i^{1})}$

Step 1.5.2.4.3.2.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = 5 \frac{- 2 - 3.46410161 i}{1 + 1.7320508 i - 1.7320508 i - 3 i^{1 + 1}}$

Step 1.5.2.4.3.2.8

Add $1$ and $1$ .

$y = 5 \frac{- 2 - 3.46410161 i}{1 + 1.7320508 i - 1.7320508 i - 3 i^{2}}$

Step 1.5.2.4.3.2.9

Subtract $1.7320508 i$ from $1.7320508 i$ .

$y = 5 \frac{- 2 - 3.46410161 i}{1 + 0 i - 3 i^{2}}$

Step 1.5.2.4.3.3

Simplify each term.

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Step 1.5.2.4.3.3.1

Multiply $0$ by $i$ .

$y = 5 \frac{- 2 - 3.46410161 i}{1 + 0 - 3 i^{2}}$

Step 1.5.2.4.3.3.2

Rewrite $i^{2}$ as $- 1$ .

$y = 5 \frac{- 2 - 3.46410161 i}{1 + 0 - 3 \cdot - 1}$

Step 1.5.2.4.3.3.3

Multiply $- 3$ by $- 1$ .

$y = 5 \frac{- 2 - 3.46410161 i}{1 + 0 + 3}$

Step 1.5.2.4.3.4

Add $1$ and $0$ .

$y = 5 \frac{- 2 - 3.46410161 i}{1 + 3}$

Step 1.5.2.4.3.5

Add $1$ and $3$ .

$y = 5 \frac{- 2 - 3.46410161 i}{4}$

Step 1.5.2.5

Rewrite $- 2$ as $1 (- 2)$ .

$y = 5 \frac{1 (- 2) - 3.46410161 i}{4}$

Step 1.5.2.6

Factor $1$ out of $- 3.46410161 i$ .

$y = 5 \frac{1 (- 2) + 1 (- 3.46410161 i)}{4}$

Step 1.5.2.7

Factor $1$ out of $1 (- 2) + 1 (- 3.46410161 i)$ .

$y = 5 \frac{1 (- 2 - 3.46410161 i)}{4}$

Step 1.5.2.8

Factor $4$ out of $4$ .

$y = 5 \frac{1 (- 2 - 3.46410161 i)}{4 (1)}$

Step 1.5.2.9

Separate fractions.

$y = 5 (\frac{1}{4} \cdot \frac{- 2 - 3.46410161 i}{1})$

Step 1.5.2.10

Simplify the expression.

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Step 1.5.2.10.1

Divide $1$ by $4$ .

$y = 5 (0.25 \frac{- 2 - 3.46410161 i}{1})$

Step 1.5.2.10.2

Divide $- 2 - 3.46410161 i$ by $1$ .

$y = 5 (0.25 (- 2 - 3.46410161 i))$

Step 1.5.2.11

Apply the distributive property.

$y = 5 (0.25 \cdot - 2 + 0.25 (- 3.46410161 i))$

Step 1.5.2.12

Multiply.

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Step 1.5.2.12.1

Multiply $0.25$ by $- 2$ .

$y = 5 (- 0.5 + 0.25 (- 3.46410161 i))$

Step 1.5.2.12.2

Multiply $- 3.46410161$ by $0.25$ .

$y = 5 (- 0.5 - 0.8660254 i)$

Step 1.5.2.13

Apply the distributive property.

$y = 5 \cdot - 0.5 + 5 (- 0.8660254 i)$

Step 1.5.2.14

Multiply.

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Step 1.5.2.14.1

Multiply $5$ by $- 0.5$ .

$y = - 2.5 + 5 (- 0.8660254 i)$

Step 1.5.2.14.2

Multiply $- 0.8660254$ by $5$ .

$y = - 2.5 - 4.33012701 i$

Step 1.6

List all of the solutions.

$y = 5, x = 1$

$y = - 2.5 + 4.33012701 i, x = - \frac{1 - i \sqrt{3}}{2}$

$y = - 2.5 - 4.33012701 i, x = - \frac{1 + i \sqrt{3}}{2}$

$y = 5, x = 1$

$y = - 2.5 + 4.33012701 i, x = - \frac{1 - i \sqrt{3}}{2}$

$y = - 2.5 - 4.33012701 i, x = - \frac{1 + i \sqrt{3}}{2}$

Step 2

The area between the given curves is unbounded.

Unbounded area

Step 3