Algebra Examples

$(11 i^{4} + 4 i^{3}) - (2 i^{4} - 6 i^{3})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{4}$ as $1$ .

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Step 1.1.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$11 {(i^{2})}^{2} + 4 i^{3} - (2 i^{4} - 6 i^{3})$

Step 1.1.2

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

$11 {(- 1)}^{2} + 4 i^{3} - (2 i^{4} - 6 i^{3})$

Step 1.1.3

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

$11 \cdot 1 + 4 i^{3} - (2 i^{4} - 6 i^{3})$

$11 \cdot 1 + 4 i^{3} - (2 i^{4} - 6 i^{3})$

Step 1.2

Multiply $11$ by $1$ .

$11 + 4 i^{3} - (2 i^{4} - 6 i^{3})$

Step 1.3

Factor out $i^{2}$ .

$11 + 4 (i^{2} \cdot i) - (2 i^{4} - 6 i^{3})$

Step 1.4

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

$11 + 4 (- 1 \cdot i) - (2 i^{4} - 6 i^{3})$

Step 1.5

Rewrite $- 1 i$ as $- i$ .

$11 + 4 (- i) - (2 i^{4} - 6 i^{3})$

Step 1.6

Multiply $- 1$ by $4$ .

$11 - 4 i - (2 i^{4} - 6 i^{3})$

Step 1.7

Simplify each term.

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Step 1.7.1

Rewrite $i^{4}$ as $1$ .

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Step 1.7.1.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$11 - 4 i - (2 {(i^{2})}^{2} - 6 i^{3})$

Step 1.7.1.2

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

$11 - 4 i - (2 {(- 1)}^{2} - 6 i^{3})$

Step 1.7.1.3

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

$11 - 4 i - (2 \cdot 1 - 6 i^{3})$

$11 - 4 i - (2 \cdot 1 - 6 i^{3})$

Step 1.7.2

Multiply $2$ by $1$ .

$11 - 4 i - (2 - 6 i^{3})$

Step 1.7.3

Factor out $i^{2}$ .

$11 - 4 i - (2 - 6 (i^{2} \cdot i))$

Step 1.7.4

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

$11 - 4 i - (2 - 6 (- 1 \cdot i))$

Step 1.7.5

Rewrite $- 1 i$ as $- i$ .

$11 - 4 i - (2 - 6 (- i))$

Step 1.7.6

Multiply $- 1$ by $- 6$ .

$11 - 4 i - (2 + 6 i)$

$11 - 4 i - (2 + 6 i)$

Step 1.8

Apply the distributive property.

$11 - 4 i - 1 \cdot 2 - (6 i)$

Step 1.9

Multiply $- 1$ by $2$ .

$11 - 4 i - 2 - (6 i)$

Step 1.10

Multiply $6$ by $- 1$ .

$11 - 4 i - 2 - 6 i$

$11 - 4 i - 2 - 6 i$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2$ from $11$ .

$9 - 4 i - 6 i$

Step 2.2

Subtract $6 i$ from $- 4 i$ .

$9 - 10 i$

$9 - 10 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$