Basic Math Examples

$i^{16} + i^{6} - 2 i^{5} + i^{13}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{16}$ as ${(i^{4})}^{4}$ .

${(i^{4})}^{4} + i^{6} - 2 i^{5} + i^{13}$

Step 1.2

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

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Step 1.2.1

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

${({(i^{2})}^{2})}^{4} + i^{6} - 2 i^{5} + i^{13}$

Step 1.2.2

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

${({(- 1)}^{2})}^{4} + i^{6} - 2 i^{5} + i^{13}$

Step 1.2.3

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

$1^{4} + i^{6} - 2 i^{5} + i^{13}$

$1^{4} + i^{6} - 2 i^{5} + i^{13}$

Step 1.3

One to any power is one.

$1 + i^{6} - 2 i^{5} + i^{13}$

Step 1.4

Factor out $i^{4}$ .

$1 + i^{4} i^{2} - 2 i^{5} + i^{13}$

Step 1.5

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

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Step 1.5.1

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

$1 + {(i^{2})}^{2} i^{2} - 2 i^{5} + i^{13}$

Step 1.5.2

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

$1 + {(- 1)}^{2} i^{2} - 2 i^{5} + i^{13}$

Step 1.5.3

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

$1 + 1 i^{2} - 2 i^{5} + i^{13}$

$1 + 1 i^{2} - 2 i^{5} + i^{13}$

Step 1.6

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

$1 + i^{2} - 2 i^{5} + i^{13}$

Step 1.7

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

$1 - 1 - 2 i^{5} + i^{13}$

Step 1.8

Factor out $i^{4}$ .

$1 - 1 - 2 (i^{4} i) + i^{13}$

Step 1.9

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

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Step 1.9.1

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

$1 - 1 - 2 ({(i^{2})}^{2} i) + i^{13}$

Step 1.9.2

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

$1 - 1 - 2 ({(- 1)}^{2} i) + i^{13}$

Step 1.9.3

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

$1 - 1 - 2 (1 i) + i^{13}$

$1 - 1 - 2 (1 i) + i^{13}$

Step 1.10

Multiply $i$ by $1$ .

$1 - 1 - 2 i + i^{13}$

Step 1.11

Rewrite $i^{13}$ as ${(i^{4})}^{3} i$ .

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Step 1.11.1

Factor out $i^{12}$ .

$1 - 1 - 2 i + i^{12} i$

Step 1.11.2

Rewrite $i^{12}$ as ${(i^{4})}^{3}$ .

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

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

Step 1.12

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

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Step 1.12.1

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

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

Step 1.12.2

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

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

Step 1.12.3

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

$1 - 1 - 2 i + 1^{3} i$

$1 - 1 - 2 i + 1^{3} i$

Step 1.13

One to any power is one.

$1 - 1 - 2 i + 1 i$

Step 1.14

Multiply $i$ by $1$ .

$1 - 1 - 2 i + i$

$1 - 1 - 2 i + i$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $1$ from $1$ .

$0 - 2 i + i$

Step 2.2

Subtract $2 i$ from $0$ .

$- 2 i + i$

Step 2.3

Add $- 2 i$ and $i$ .

$- i$

$- i$

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