Precalculus Examples

$i + i^{2} + i^{3} + i^{4} + i^{5}$

Step 1

Simplify each term.

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Step 1.1

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

$i - 1 + i^{3} + i^{4} + i^{5}$

Step 1.2

Factor out $i^{2}$ .

$i - 1 + i^{2} \cdot i + i^{4} + i^{5}$

Step 1.3

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

$i - 1 - 1 \cdot i + i^{4} + i^{5}$

Step 1.4

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

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

Step 1.5

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

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Step 1.5.1

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

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

Step 1.5.2

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

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

Step 1.5.3

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

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

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

Step 1.6

Factor out $i^{4}$ .

$i - 1 - i + 1 + i^{4} i$

Step 1.7

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

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Step 1.7.1

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

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

Step 1.7.2

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

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

Step 1.7.3

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

$i - 1 - i + 1 + 1 i$

$i - 1 - i + 1 + 1 i$

Step 1.8

Multiply $i$ by $1$ .

$i - 1 - i + 1 + i$

$i - 1 - i + 1 + i$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $i$ from $i$ .

$0 - 1 + 1 + i$

Step 2.2

Simplify by adding and subtracting.

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Step 2.2.1

Subtract $1$ from $0$ .

$- 1 + 1 + i$

Step 2.2.2

Add $- 1$ and $1$ .

$0 + i$

Step 2.2.3

Add $0$ and $i$ .

$i$

$i$

$i$

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