Finite Math Examples

$i^{137} + i^{1003}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{137}$ as ${(i^{4})}^{34} i$ .

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Step 1.1.1

Factor out $i^{136}$ .

$i^{136} i + i^{1003}$

Step 1.1.2

Rewrite $i^{136}$ as ${(i^{4})}^{34}$ .

${(i^{4})}^{34} i + i^{1003}$

${(i^{4})}^{34} i + i^{1003}$

Step 1.2

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

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Step 1.2.1

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

${({(i^{2})}^{2})}^{34} i + i^{1003}$

Step 1.2.2

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

${({(- 1)}^{2})}^{34} i + i^{1003}$

Step 1.2.3

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

$1^{34} i + i^{1003}$

$1^{34} i + i^{1003}$

Step 1.3

One to any power is one.

$1 i + i^{1003}$

Step 1.4

Multiply $i$ by $1$ .

$i + i^{1003}$

Step 1.5

Rewrite $i^{1003}$ as ${(i^{4})}^{250} (i^{2} \cdot i)$ .

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Step 1.5.1

Factor out $i^{1000}$ .

$i + i^{1000} i^{3}$

Step 1.5.2

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

$i + {(i^{4})}^{250} i^{3}$

Step 1.5.3

Factor out $i^{2}$ .

$i + {(i^{4})}^{250} (i^{2} \cdot i)$

$i + {(i^{4})}^{250} (i^{2} \cdot i)$

Step 1.6

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

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Step 1.6.1

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

$i + {({(i^{2})}^{2})}^{250} (i^{2} \cdot i)$

Step 1.6.2

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

$i + {({(- 1)}^{2})}^{250} (i^{2} \cdot i)$

Step 1.6.3

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

$i + 1^{250} (i^{2} \cdot i)$

$i + 1^{250} (i^{2} \cdot i)$

Step 1.7

One to any power is one.

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

Step 1.8

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

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

Step 1.9

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

$i - 1 \cdot i$

Step 1.10

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

$i - i$

$i - i$

Step 2

Subtract $i$ from $i$ .

$0$

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