Basic Math Examples

$i^{221} + i^{335}$

Step 1

Rewrite $i^{221}$ as ${(i^{4})}^{55} i$ .

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Step 1.1

Factor out $i^{220}$ .

$i^{220} i + i^{335}$

Step 1.2

Rewrite $i^{220}$ as ${(i^{4})}^{55}$ .

${(i^{4})}^{55} i + i^{335}$

${(i^{4})}^{55} i + i^{335}$

Step 2

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

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Step 2.1

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

${({(i^{2})}^{2})}^{55} i + i^{335}$

Step 2.2

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

${({(- 1)}^{2})}^{55} i + i^{335}$

Step 2.3

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

$1^{55} i + i^{335}$

$1^{55} i + i^{335}$

Step 3

One to any power is one.

$1 i + i^{335}$

Step 4

Multiply $i$ by $1$ .

$i + i^{335}$

Step 5

Rewrite $i^{335}$ as ${(i^{4})}^{83} (i^{2} \cdot i)$ .

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Step 5.1

Factor out $i^{332}$ .

$i + i^{332} i^{3}$

Step 5.2

Rewrite $i^{332}$ as ${(i^{4})}^{83}$ .

$i + {(i^{4})}^{83} i^{3}$

Step 5.3

Factor out $i^{2}$ .

$i + {(i^{4})}^{83} (i^{2} i)$

Step 5.4

Add multiplication sign between $i$ and $i^{2}$ .

$i + {(i^{4})}^{83} (i^{2} \cdot i)$

$i + {(i^{4})}^{83} (i^{2} \cdot i)$

Step 6

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

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Step 6.1

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

$i + {({(i^{2})}^{2})}^{83} (i^{2} \cdot i)$

Step 6.2

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

$i + {({(- 1)}^{2})}^{83} (i^{2} \cdot i)$

Step 6.3

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

$i + 1^{83} (i^{2} \cdot i)$

$i + 1^{83} (i^{2} \cdot i)$

Step 7

One to any power is one.

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

Step 8

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

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

Step 9

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

$i - 1 i$

Step 10

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

$i - i$

Step 11

Subtract $i$ from $i$ .

$0$

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