Precalculus Examples

$i^{46} + i^{47}$

Step 1

Rewrite $i^{46}$ as ${(i^{4})}^{11} i^{2}$ .

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Step 1.1

Factor out $i^{44}$ .

$i^{44} i^{2} + i^{47}$

Step 1.2

Rewrite $i^{44}$ as ${(i^{4})}^{11}$ .

${(i^{4})}^{11} i^{2} + i^{47}$

${(i^{4})}^{11} i^{2} + i^{47}$

Step 2

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

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Step 2.1

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

${({(i^{2})}^{2})}^{11} i^{2} + i^{47}$

Step 2.2

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

${({(- 1)}^{2})}^{11} i^{2} + i^{47}$

Step 2.3

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

$1^{11} i^{2} + i^{47}$

$1^{11} i^{2} + i^{47}$

Step 3

One to any power is one.

$1 i^{2} + i^{47}$

Step 4

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

$i^{2} + i^{47}$

Step 5

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

$- 1 + i^{47}$

Step 6

Rewrite $i^{47}$ as ${(i^{4})}^{11} (i^{2} \cdot i)$ .

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Step 6.1

Factor out $i^{44}$ .

$- 1 + i^{44} i^{3}$

Step 6.2

Rewrite $i^{44}$ as ${(i^{4})}^{11}$ .

$- 1 + {(i^{4})}^{11} i^{3}$

Step 6.3

Factor out $i^{2}$ .

$- 1 + {(i^{4})}^{11} (i^{2} \cdot i)$

$- 1 + {(i^{4})}^{11} (i^{2} \cdot i)$

Step 7

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

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Step 7.1

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

$- 1 + {({(i^{2})}^{2})}^{11} (i^{2} \cdot i)$

Step 7.2

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

$- 1 + {({(- 1)}^{2})}^{11} (i^{2} \cdot i)$

Step 7.3

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

$- 1 + 1^{11} (i^{2} \cdot i)$

$- 1 + 1^{11} (i^{2} \cdot i)$

Step 8

One to any power is one.

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

Step 9

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

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

Step 10

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

$- 1 - 1 \cdot i$

Step 11

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

$- 1 - i$

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