Basic Math Examples

$3 i^{36} + 4 i^{102} - i^{201}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{36}$ as ${(i^{4})}^{9}$ .

$3 {(i^{4})}^{9} + 4 i^{102} - i^{201}$

Step 1.2

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

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Step 1.2.1

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

$3 {({(i^{2})}^{2})}^{9} + 4 i^{102} - i^{201}$

Step 1.2.2

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

$3 {({(- 1)}^{2})}^{9} + 4 i^{102} - i^{201}$

Step 1.2.3

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

$3 \cdot 1^{9} + 4 i^{102} - i^{201}$

$3 \cdot 1^{9} + 4 i^{102} - i^{201}$

Step 1.3

One to any power is one.

$3 \cdot 1 + 4 i^{102} - i^{201}$

Step 1.4

Multiply $3$ by $1$ .

$3 + 4 i^{102} - i^{201}$

Step 1.5

Rewrite $i^{102}$ as ${(i^{4})}^{25} i^{2}$ .

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Step 1.5.1

Factor out $i^{100}$ .

$3 + 4 (i^{100} i^{2}) - i^{201}$

Step 1.5.2

Rewrite $i^{100}$ as ${(i^{4})}^{25}$ .

$3 + 4 ({(i^{4})}^{25} i^{2}) - i^{201}$

$3 + 4 ({(i^{4})}^{25} i^{2}) - i^{201}$

Step 1.6

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

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Step 1.6.1

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

$3 + 4 ({({(i^{2})}^{2})}^{25} i^{2}) - i^{201}$

Step 1.6.2

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

$3 + 4 ({({(- 1)}^{2})}^{25} i^{2}) - i^{201}$

Step 1.6.3

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

$3 + 4 (1^{25} i^{2}) - i^{201}$

$3 + 4 (1^{25} i^{2}) - i^{201}$

Step 1.7

One to any power is one.

$3 + 4 (1 i^{2}) - i^{201}$

Step 1.8

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

$3 + 4 i^{2} - i^{201}$

Step 1.9

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

$3 + 4 \cdot - 1 - i^{201}$

Step 1.10

Multiply $4$ by $- 1$ .

$3 - 4 - i^{201}$

Step 1.11

Rewrite $i^{201}$ as ${(i^{4})}^{50} i$ .

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Step 1.11.1

Factor out $i^{200}$ .

$3 - 4 - (i^{200} i)$

Step 1.11.2

Rewrite $i^{200}$ as ${(i^{4})}^{50}$ .

$3 - 4 - ({(i^{4})}^{50} i)$

$3 - 4 - ({(i^{4})}^{50} i)$

Step 1.12

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

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Step 1.12.1

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

$3 - 4 - ({({(i^{2})}^{2})}^{50} i)$

Step 1.12.2

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

$3 - 4 - ({({(- 1)}^{2})}^{50} i)$

Step 1.12.3

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

$3 - 4 - (1^{50} i)$

$3 - 4 - (1^{50} i)$

Step 1.13

One to any power is one.

$3 - 4 - (1 i)$

Step 1.14

Multiply $i$ by $1$ .

$3 - 4 - i$

$3 - 4 - i$

Step 2

Subtract $4$ from $3$ .

$- 1 - i$

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