Precalculus Examples

$4 + 7 i^{22} + 3 - 6 i^{32}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{22}$ as ${(i^{4})}^{5} i^{2}$ .

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Step 1.1.1

Factor out $i^{20}$ .

$4 + 7 (i^{20} i^{2}) + 3 - 6 i^{32}$

Step 1.1.2

Rewrite $i^{20}$ as ${(i^{4})}^{5}$ .

$4 + 7 ({(i^{4})}^{5} i^{2}) + 3 - 6 i^{32}$

$4 + 7 ({(i^{4})}^{5} i^{2}) + 3 - 6 i^{32}$

Step 1.2

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

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Step 1.2.1

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

$4 + 7 ({({(i^{2})}^{2})}^{5} i^{2}) + 3 - 6 i^{32}$

Step 1.2.2

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

$4 + 7 ({({(- 1)}^{2})}^{5} i^{2}) + 3 - 6 i^{32}$

Step 1.2.3

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

$4 + 7 (1^{5} i^{2}) + 3 - 6 i^{32}$

$4 + 7 (1^{5} i^{2}) + 3 - 6 i^{32}$

Step 1.3

One to any power is one.

$4 + 7 (1 i^{2}) + 3 - 6 i^{32}$

Step 1.4

Multiply $i^{2}$ by $1$ .

$4 + 7 i^{2} + 3 - 6 i^{32}$

Step 1.5

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

$4 + 7 \cdot - 1 + 3 - 6 i^{32}$

Step 1.6

Multiply $7$ by $- 1$ .

$4 - 7 + 3 - 6 i^{32}$

Step 1.7

Rewrite $i^{32}$ as ${(i^{4})}^{8}$ .

$4 - 7 + 3 - 6 {(i^{4})}^{8}$

Step 1.8

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

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Step 1.8.1

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

$4 - 7 + 3 - 6 {({(i^{2})}^{2})}^{8}$

Step 1.8.2

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

$4 - 7 + 3 - 6 {({(- 1)}^{2})}^{8}$

Step 1.8.3

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

$4 - 7 + 3 - 6 \cdot 1^{8}$

$4 - 7 + 3 - 6 \cdot 1^{8}$

Step 1.9

One to any power is one.

$4 - 7 + 3 - 6 \cdot 1$

Step 1.10

Multiply $- 6$ by $1$ .

$4 - 7 + 3 - 6$

$4 - 7 + 3 - 6$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Subtract $7$ from $4$ .

$- 3 + 3 - 6$

Step 2.2

Add $- 3$ and $3$ .

$0 - 6$

Step 2.3

Subtract $6$ from $0$ .

$- 6$

$- 6$

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