Precalculus Examples

$i^{1002}$

Step 1

Rewrite $i^{1002}$ as ${(i^{4})}^{250} i^{2}$ .

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Step 1.1

Factor out $i^{1000}$ .

$i^{1000} i^{2}$

Step 1.2

Rewrite $i^{1000}$ as ${(i^{4})}^{250}$ .

${(i^{4})}^{250} i^{2}$

${(i^{4})}^{250} i^{2}$

Step 2

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

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Step 2.1

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

${({(i^{2})}^{2})}^{250} i^{2}$

Step 2.2

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

${({(- 1)}^{2})}^{250} i^{2}$

Step 2.3

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

$1^{250} i^{2}$

$1^{250} i^{2}$

Step 3

One to any power is one.

$1 i^{2}$

Step 4

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

$i^{2}$

Step 5

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

$- 1$

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