Basic Math Examples

$4 + i^{17} + i^{18} + i^{19} + i^{20}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{17}$ as ${(i^{4})}^{4} i$ .

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Step 1.1.1

Factor out $i^{16}$ .

$4 + i^{16} i + i^{18} + i^{19} + i^{20}$

Step 1.1.2

Rewrite $i^{16}$ as ${(i^{4})}^{4}$ .

$4 + {(i^{4})}^{4} i + i^{18} + i^{19} + i^{20}$

Step 1.2

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

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Step 1.2.1

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

$4 + {({(i^{2})}^{2})}^{4} i + i^{18} + i^{19} + i^{20}$

Step 1.2.2

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

$4 + {({(- 1)}^{2})}^{4} i + i^{18} + i^{19} + i^{20}$

Step 1.2.3

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

$4 + 1^{4} i + i^{18} + i^{19} + i^{20}$

Step 1.3

One to any power is one.

$4 + 1 i + i^{18} + i^{19} + i^{20}$

Step 1.4

Multiply $i$ by $1$ .

$4 + i + i^{18} + i^{19} + i^{20}$

Step 1.5

Rewrite $i^{18}$ as ${(i^{4})}^{4} i^{2}$ .

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Step 1.5.1

Factor out $i^{16}$ .

$4 + i + i^{16} i^{2} + i^{19} + i^{20}$

Step 1.5.2

Rewrite $i^{16}$ as ${(i^{4})}^{4}$ .

$4 + i + {(i^{4})}^{4} i^{2} + i^{19} + i^{20}$

Step 1.6

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

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Step 1.6.1

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

$4 + i + {({(i^{2})}^{2})}^{4} i^{2} + i^{19} + i^{20}$

Step 1.6.2

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

$4 + i + {({(- 1)}^{2})}^{4} i^{2} + i^{19} + i^{20}$

Step 1.6.3

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

$4 + i + 1^{4} i^{2} + i^{19} + i^{20}$

Step 1.7

One to any power is one.

$4 + i + 1 i^{2} + i^{19} + i^{20}$

Step 1.8

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

$4 + i + i^{2} + i^{19} + i^{20}$

Step 1.9

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

$4 + i - 1 + i^{19} + i^{20}$

Step 1.10

Rewrite $i^{19}$ as ${(i^{4})}^{4} (i^{2} \cdot i)$ .

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Step 1.10.1

Factor out $i^{16}$ .

$4 + i - 1 + i^{16} i^{3} + i^{20}$

Step 1.10.2

Rewrite $i^{16}$ as ${(i^{4})}^{4}$ .

$4 + i - 1 + {(i^{4})}^{4} i^{3} + i^{20}$

Step 1.10.3

Factor out $i^{2}$ .

$4 + i - 1 + {(i^{4})}^{4} (i^{2} \cdot i) + i^{20}$

Step 1.11

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

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Step 1.11.1

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

$4 + i - 1 + {({(i^{2})}^{2})}^{4} (i^{2} \cdot i) + i^{20}$

Step 1.11.2

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

$4 + i - 1 + {({(- 1)}^{2})}^{4} (i^{2} \cdot i) + i^{20}$

Step 1.11.3

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

$4 + i - 1 + 1^{4} (i^{2} \cdot i) + i^{20}$

Step 1.12

One to any power is one.

$4 + i - 1 + 1 (i^{2} \cdot i) + i^{20}$

Step 1.13

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

$4 + i - 1 + i^{2} \cdot i + i^{20}$

Step 1.14

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

$4 + i - 1 - 1 \cdot i + i^{20}$

Step 1.15

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

$4 + i - 1 - i + i^{20}$

Step 1.16

Rewrite $i^{20}$ as ${(i^{4})}^{5}$ .

$4 + i - 1 - i + {(i^{4})}^{5}$

Step 1.17

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

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Step 1.17.1

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

$4 + i - 1 - i + {({(i^{2})}^{2})}^{5}$

Step 1.17.2

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

$4 + i - 1 - i + {({(- 1)}^{2})}^{5}$

Step 1.17.3

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

$4 + i - 1 - i + 1^{5}$

Step 1.18

One to any power is one.

$4 + i - 1 - i + 1$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $1$ from $4$ .

$3 + i - i + 1$

Step 2.2

Add $3$ and $1$ .

$4 + i - i$

Step 2.3

Subtract $i$ from $i$ .

$4 + 0$

Step 2.4

Add $4$ and $0$ .

$4$