Basic Math Examples

15 i^{100} - 2 i^{401} + 4 i^{38} - 7 i^{75}

$15 i^{100} - 2 i^{401} + 4 i^{38} - 7 i^{75}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

i^{100}

$i^{100}$ as

{(i^{4})}^{25}

${(i^{4})}^{25}$ .

15 {(i^{4})}^{25} - 2 i^{401} + 4 i^{38} - 7 i^{75}

$15 {(i^{4})}^{25} - 2 i^{401} + 4 i^{38} - 7 i^{75}$

Step 1.2

Rewrite

i^{4}

$i^{4}$ as

1

$1$ .

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Step 1.2.1

Rewrite

i^{4}

$i^{4}$ as

{(i^{2})}^{2}

${(i^{2})}^{2}$ .

15 {({(i^{2})}^{2})}^{25} - 2 i^{401} + 4 i^{38} - 7 i^{75}

$15 {({(i^{2})}^{2})}^{25} - 2 i^{401} + 4 i^{38} - 7 i^{75}$

Step 1.2.2

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

15 {({(- 1)}^{2})}^{25} - 2 i^{401} + 4 i^{38} - 7 i^{75}

$15 {({(- 1)}^{2})}^{25} - 2 i^{401} + 4 i^{38} - 7 i^{75}$

Step 1.2.3

Raise

- 1

$- 1$ to the power of

2

$2$ .

15 \cdot 1^{25} - 2 i^{401} + 4 i^{38} - 7 i^{75}

$15 \cdot 1^{25} - 2 i^{401} + 4 i^{38} - 7 i^{75}$

15 \cdot 1^{25} - 2 i^{401} + 4 i^{38} - 7 i^{75}

$15 \cdot 1^{25} - 2 i^{401} + 4 i^{38} - 7 i^{75}$

Step 1.3

One to any power is one.

15 \cdot 1 - 2 i^{401} + 4 i^{38} - 7 i^{75}

$15 \cdot 1 - 2 i^{401} + 4 i^{38} - 7 i^{75}$

Step 1.4

Multiply

15

$15$ by

1

$1$ .

15 - 2 i^{401} + 4 i^{38} - 7 i^{75}

$15 - 2 i^{401} + 4 i^{38} - 7 i^{75}$

Step 1.5

Rewrite

i^{401}

$i^{401}$ as

{(i^{4})}^{100} i

${(i^{4})}^{100} i$ .

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Step 1.5.1

Factor out

i^{400}

$i^{400}$ .

15 - 2 (i^{400} i) + 4 i^{38} - 7 i^{75}

$15 - 2 (i^{400} i) + 4 i^{38} - 7 i^{75}$

Step 1.5.2

Rewrite

i^{400}

$i^{400}$ as

{(i^{4})}^{100}

${(i^{4})}^{100}$ .

15 - 2 ({(i^{4})}^{100} i) + 4 i^{38} - 7 i^{75}

$15 - 2 ({(i^{4})}^{100} i) + 4 i^{38} - 7 i^{75}$

15 - 2 ({(i^{4})}^{100} i) + 4 i^{38} - 7 i^{75}

$15 - 2 ({(i^{4})}^{100} i) + 4 i^{38} - 7 i^{75}$

Step 1.6

Rewrite

i^{4}

$i^{4}$ as

1

$1$ .

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Step 1.6.1

Rewrite

i^{4}

$i^{4}$ as

{(i^{2})}^{2}

${(i^{2})}^{2}$ .

$15 - 2 ({({(i^{2})}^{2})}^{100} i) + 4 i^{38} - 7 i^{75}$

Step 1.6.2

Rewrite

$i^{2}$ as

$- 1$ .

$15 - 2 ({({(- 1)}^{2})}^{100} i) + 4 i^{38} - 7 i^{75}$

Step 1.6.3

Raise

$- 1$ to the power of

$2$ .

$15 - 2 (1^{100} i) + 4 i^{38} - 7 i^{75}$

Step 1.7

One to any power is one.

$15 - 2 (1 i) + 4 i^{38} - 7 i^{75}$

Step 1.8

Multiply

$i$ by

$1$ .

$15 - 2 i + 4 i^{38} - 7 i^{75}$

Step 1.9

Rewrite

$i^{38}$ as

${(i^{4})}^{9} i^{2}$ .

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Step 1.9.1

Factor out

$i^{36}$ .

$15 - 2 i + 4 (i^{36} i^{2}) - 7 i^{75}$

Step 1.9.2

Rewrite

$i^{36}$ as

${(i^{4})}^{9}$ .

$15 - 2 i + 4 ({(i^{4})}^{9} i^{2}) - 7 i^{75}$

Step 1.10

Rewrite

$i^{4}$ as

$1$ .

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Step 1.10.1

Rewrite

$i^{4}$ as

${(i^{2})}^{2}$ .

$15 - 2 i + 4 ({({(i^{2})}^{2})}^{9} i^{2}) - 7 i^{75}$

Step 1.10.2

Rewrite

$i^{2}$ as

$- 1$ .

$15 - 2 i + 4 ({({(- 1)}^{2})}^{9} i^{2}) - 7 i^{75}$

Step 1.10.3

Raise

$- 1$ to the power of

$2$ .

$15 - 2 i + 4 (1^{9} i^{2}) - 7 i^{75}$

Step 1.11

One to any power is one.

$15 - 2 i + 4 (1 i^{2}) - 7 i^{75}$

Step 1.12

Multiply

$i^{2}$ by

$1$ .

$15 - 2 i + 4 i^{2} - 7 i^{75}$

Step 1.13

Rewrite

$i^{2}$ as

$- 1$ .

$15 - 2 i + 4 \cdot - 1 - 7 i^{75}$

Step 1.14

Multiply

$4$ by

$- 1$ .

$15 - 2 i - 4 - 7 i^{75}$

Step 1.15

Rewrite

$i^{75}$ as

${(i^{4})}^{18} (i^{2} \cdot i)$ .

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Step 1.15.1

Factor out

$i^{72}$ .

$15 - 2 i - 4 - 7 (i^{72} i^{3})$

Step 1.15.2

Rewrite

$i^{72}$ as

${(i^{4})}^{18}$ .

$15 - 2 i - 4 - 7 ({(i^{4})}^{18} i^{3})$

Step 1.15.3

Factor out

$i^{2}$ .

$15 - 2 i - 4 - 7 ({(i^{4})}^{18} (i^{2} \cdot i))$

Step 1.16

Rewrite

$i^{4}$ as

$1$ .

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Step 1.16.1

Rewrite

$i^{4}$ as

${(i^{2})}^{2}$ .

$15 - 2 i - 4 - 7 ({({(i^{2})}^{2})}^{18} (i^{2} \cdot i))$

Step 1.16.2

Rewrite

$i^{2}$ as

$- 1$ .

$15 - 2 i - 4 - 7 ({({(- 1)}^{2})}^{18} (i^{2} \cdot i))$

Step 1.16.3

Raise

$- 1$ to the power of

$2$ .

$15 - 2 i - 4 - 7 (1^{18} (i^{2} \cdot i))$

Step 1.17

One to any power is one.

$15 - 2 i - 4 - 7 (1 (i^{2} \cdot i))$

Step 1.18

Multiply

$i^{2} \cdot i$ by

$1$ .

$15 - 2 i - 4 - 7 (i^{2} \cdot i)$

Step 1.19

Rewrite

$i^{2}$ as

$- 1$ .

$15 - 2 i - 4 - 7 (- 1 \cdot i)$

Step 1.20

Rewrite

$- 1 i$ as

$- i$ .

$15 - 2 i - 4 - 7 (- i)$

Step 1.21

Multiply

$- 1$ by

$- 7$ .

$15 - 2 i - 4 + 7 i$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract

$4$ from

$15$ .

$11 - 2 i + 7 i$

Step 2.2

Add

$- 2 i$ and

$7 i$ .

$11 + 5 i$