Algebra Examples

$i^{3} + i^{5} + i^{7} + i^{9}$

Step 1

Simplify each term.

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Step 1.1

Factor out $i^{2}$ .

$i^{2} \cdot i + i^{5} + i^{7} + i^{9}$

Step 1.2

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

$- 1 \cdot i + i^{5} + i^{7} + i^{9}$

Step 1.3

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

$- i + i^{5} + i^{7} + i^{9}$

Step 1.4

Factor out $i^{4}$ .

$- i + i^{4} i + i^{7} + i^{9}$

Step 1.5

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

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Step 1.5.1

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

$- i + {(i^{2})}^{2} i + i^{7} + i^{9}$

Step 1.5.2

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

$- i + {(- 1)}^{2} i + i^{7} + i^{9}$

Step 1.5.3

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

$- i + 1 i + i^{7} + i^{9}$

$- i + 1 i + i^{7} + i^{9}$

Step 1.6

Multiply $i$ by $1$ .

$- i + i + i^{7} + i^{9}$

Step 1.7

Rewrite $i^{7}$ as $i^{4} (i^{2} \cdot i)$ .

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Step 1.7.1

Factor out $i^{4}$ .

$- i + i + i^{4} i^{3} + i^{9}$

Step 1.7.2

Factor out $i^{2}$ .

$- i + i + i^{4} (i^{2} \cdot i) + i^{9}$

$- i + i + i^{4} (i^{2} \cdot i) + i^{9}$

Step 1.8

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

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Step 1.8.1

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

$- i + i + {(i^{2})}^{2} (i^{2} \cdot i) + i^{9}$

Step 1.8.2

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

$- i + i + {(- 1)}^{2} (i^{2} \cdot i) + i^{9}$

Step 1.8.3

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

$- i + i + 1 (i^{2} \cdot i) + i^{9}$

$- i + i + 1 (i^{2} \cdot i) + i^{9}$

Step 1.9

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

$- i + i + i^{2} \cdot i + i^{9}$

Step 1.10

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

$- i + i - 1 \cdot i + i^{9}$

Step 1.11

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

$- i + i - i + i^{9}$

Step 1.12

Rewrite $i^{9}$ as ${(i^{4})}^{2} i$ .

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Step 1.12.1

Factor out $i^{8}$ .

$- i + i - i + i^{8} i$

Step 1.12.2

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

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

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

Step 1.13

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

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Step 1.13.1

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

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

Step 1.13.2

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

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

Step 1.13.3

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

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

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

Step 1.14

One to any power is one.

$- i + i - i + 1 i$

Step 1.15

Multiply $i$ by $1$ .

$- i + i - i + i$

$- i + i - i + i$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- i$ and $i$ .

$0 - i + i$

Step 2.2

Subtract $i$ from $0$ .

$- i + i$

Step 2.3

Add $- i$ and $i$ .

$0$

$0$

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