Basic Math Examples

$i^{39} - i^{52} + i^{75} - i^{205} + i^{60}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{39}$ as ${(i^{4})}^{9} (i^{2} \cdot i)$ .

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Step 1.1.1

Factor out $i^{36}$ .

$i^{36} i^{3} - i^{52} + i^{75} - i^{205} + i^{60}$

Step 1.1.2

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

${(i^{4})}^{9} i^{3} - i^{52} + i^{75} - i^{205} + i^{60}$

Step 1.1.3

Factor out $i^{2}$ .

${(i^{4})}^{9} (i^{2} \cdot i) - i^{52} + i^{75} - i^{205} + i^{60}$

Step 1.2

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

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Step 1.2.1

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

${({(i^{2})}^{2})}^{9} (i^{2} \cdot i) - i^{52} + i^{75} - i^{205} + i^{60}$

Step 1.2.2

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

${({(- 1)}^{2})}^{9} (i^{2} \cdot i) - i^{52} + i^{75} - i^{205} + i^{60}$

Step 1.2.3

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

$1^{9} (i^{2} \cdot i) - i^{52} + i^{75} - i^{205} + i^{60}$

Step 1.3

One to any power is one.

$1 (i^{2} \cdot i) - i^{52} + i^{75} - i^{205} + i^{60}$

Step 1.4

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

$i^{2} \cdot i - i^{52} + i^{75} - i^{205} + i^{60}$

Step 1.5

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

$- 1 \cdot i - i^{52} + i^{75} - i^{205} + i^{60}$

Step 1.6

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

$- i - i^{52} + i^{75} - i^{205} + i^{60}$

Step 1.7

Rewrite $i^{52}$ as ${(i^{4})}^{13}$ .

$- i - {(i^{4})}^{13} + i^{75} - i^{205} + i^{60}$

Step 1.8

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

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Step 1.8.1

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

$- i - {({(i^{2})}^{2})}^{13} + i^{75} - i^{205} + i^{60}$

Step 1.8.2

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

$- i - {({(- 1)}^{2})}^{13} + i^{75} - i^{205} + i^{60}$

Step 1.8.3

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

$- i - 1^{13} + i^{75} - i^{205} + i^{60}$

Step 1.9

One to any power is one.

$- i - 1 \cdot 1 + i^{75} - i^{205} + i^{60}$

Step 1.10

Multiply $- 1$ by $1$ .

$- i - 1 + i^{75} - i^{205} + i^{60}$

Step 1.11

Rewrite $i^{75}$ as ${(i^{4})}^{18} (i^{2} \cdot i)$ .

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Step 1.11.1

Factor out $i^{72}$ .

$- i - 1 + i^{72} i^{3} - i^{205} + i^{60}$

Step 1.11.2

Rewrite $i^{72}$ as ${(i^{4})}^{18}$ .

$- i - 1 + {(i^{4})}^{18} i^{3} - i^{205} + i^{60}$

Step 1.11.3

Factor out $i^{2}$ .

$- i - 1 + {(i^{4})}^{18} (i^{2} \cdot i) - i^{205} + i^{60}$

Step 1.12

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

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Step 1.12.1

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

$- i - 1 + {({(i^{2})}^{2})}^{18} (i^{2} \cdot i) - i^{205} + i^{60}$

Step 1.12.2

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

$- i - 1 + {({(- 1)}^{2})}^{18} (i^{2} \cdot i) - i^{205} + i^{60}$

Step 1.12.3

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

$- i - 1 + 1^{18} (i^{2} \cdot i) - i^{205} + i^{60}$

Step 1.13

One to any power is one.

$- i - 1 + 1 (i^{2} \cdot i) - i^{205} + i^{60}$

Step 1.14

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

$- i - 1 + i^{2} \cdot i - i^{205} + i^{60}$

Step 1.15

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

$- i - 1 - 1 \cdot i - i^{205} + i^{60}$

Step 1.16

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

$- i - 1 - i - i^{205} + i^{60}$

Step 1.17

Rewrite $i^{205}$ as ${(i^{4})}^{51} i$ .

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Step 1.17.1

Factor out $i^{204}$ .

$- i - 1 - i - (i^{204} i) + i^{60}$

Step 1.17.2

Rewrite $i^{204}$ as ${(i^{4})}^{51}$ .

$- i - 1 - i - ({(i^{4})}^{51} i) + i^{60}$

Step 1.18

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

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Step 1.18.1

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

$- i - 1 - i - ({({(i^{2})}^{2})}^{51} i) + i^{60}$

Step 1.18.2

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

$- i - 1 - i - ({({(- 1)}^{2})}^{51} i) + i^{60}$

Step 1.18.3

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

$- i - 1 - i - (1^{51} i) + i^{60}$

Step 1.19

One to any power is one.

$- i - 1 - i - (1 i) + i^{60}$

Step 1.20

Multiply $i$ by $1$ .

$- i - 1 - i - i + i^{60}$

Step 1.21

Rewrite $i^{60}$ as ${(i^{4})}^{15}$ .

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

Step 1.22

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

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Step 1.22.1

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

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

Step 1.22.2

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

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

Step 1.22.3

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

$- i - 1 - i - i + 1^{15}$

Step 1.23

One to any power is one.

$- i - 1 - i - i + 1$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $i$ from $- i$ .

$- 1 - 2 i - i + 1$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $- 1$ and $1$ .

$0 - 2 i - i$

Step 2.2.2

Subtract $2 i$ from $0$ .

$- 2 i - i$

Step 2.3

Subtract $i$ from $- 2 i$ .

$- 3 i$