Algebra Examples

$(3 - 2 i) - (x + y i) = (2 - 3 i)$

Step 1

Simplify each term.

$3 - 2 i - x - y i = 2 - 3 i$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Subtract $3$ from both sides of the equation.

$- 2 i - x - y i = 2 - 3 i - 3$

Step 2.2

Add $2 i$ to both sides of the equation.

$- x - y i = 2 - 3 i - 3 + 2 i$

Step 2.3

Add $y i$ to both sides of the equation.

$- x = 2 - 3 i - 3 + 2 i + y i$

Step 2.4

Subtract $3$ from $2$ .

$- x = - 1 - 3 i + 2 i + y i$

Step 2.5

Add $- 3 i$ and $2 i$ .

$- x = - 1 - i + y i$

Step 3

Divide each term in $- x = - 1 - i + y i$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- x = - 1 - i + y i$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 1}{- 1} + \frac{- i}{- 1} + \frac{y i}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 1}{- 1} + \frac{- i}{- 1} + \frac{y i}{- 1}$

Step 3.2.2

Divide $x$ by $1$ .

$x = \frac{- 1}{- 1} + \frac{- i}{- 1} + \frac{y i}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Divide $- 1$ by $- 1$ .

$x = 1 + \frac{- i}{- 1} + \frac{y i}{- 1}$

Step 3.3.1.2

Dividing two negative values results in a positive value.

$x = 1 + \frac{i}{1} + \frac{y i}{- 1}$

Step 3.3.1.3

Divide $i$ by $1$ .

$x = 1 + i + \frac{y i}{- 1}$

Step 3.3.1.4

Move the negative one from the denominator of $\frac{y i}{- 1}$ .

$x = 1 + i - 1 \cdot (y i)$

Step 3.3.1.5

Rewrite $- 1 \cdot (y i)$ as $- (y i)$ .

$x = 1 + i - y i$