Algebra Examples

$- 7 i^{26} + i^{74} - 2 i^{31} - 12 i^{70}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{26}$ as ${(i^{4})}^{6} i^{2}$ .

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Step 1.1.1

Factor out $i^{24}$ .

$- 7 (i^{24} i^{2}) + i^{74} - 2 i^{31} - 12 i^{70}$

Step 1.1.2

Rewrite $i^{24}$ as ${(i^{4})}^{6}$ .

$- 7 ({(i^{4})}^{6} i^{2}) + i^{74} - 2 i^{31} - 12 i^{70}$

Step 1.2

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

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Step 1.2.1

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

$- 7 ({({(i^{2})}^{2})}^{6} i^{2}) + i^{74} - 2 i^{31} - 12 i^{70}$

Step 1.2.2

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

$- 7 ({({(- 1)}^{2})}^{6} i^{2}) + i^{74} - 2 i^{31} - 12 i^{70}$

Step 1.2.3

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

$- 7 (1^{6} i^{2}) + i^{74} - 2 i^{31} - 12 i^{70}$

Step 1.3

One to any power is one.

$- 7 (1 i^{2}) + i^{74} - 2 i^{31} - 12 i^{70}$

Step 1.4

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

$- 7 i^{2} + i^{74} - 2 i^{31} - 12 i^{70}$

Step 1.5

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

$- 7 \cdot - 1 + i^{74} - 2 i^{31} - 12 i^{70}$

Step 1.6

Multiply $- 7$ by $- 1$ .

$7 + i^{74} - 2 i^{31} - 12 i^{70}$

Step 1.7

Rewrite $i^{74}$ as ${(i^{4})}^{18} i^{2}$ .

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Step 1.7.1

Factor out $i^{72}$ .

$7 + i^{72} i^{2} - 2 i^{31} - 12 i^{70}$

Step 1.7.2

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

$7 + {(i^{4})}^{18} i^{2} - 2 i^{31} - 12 i^{70}$

Step 1.8

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

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Step 1.8.1

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

$7 + {({(i^{2})}^{2})}^{18} i^{2} - 2 i^{31} - 12 i^{70}$

Step 1.8.2

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

$7 + {({(- 1)}^{2})}^{18} i^{2} - 2 i^{31} - 12 i^{70}$

Step 1.8.3

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

$7 + 1^{18} i^{2} - 2 i^{31} - 12 i^{70}$

Step 1.9

One to any power is one.

$7 + 1 i^{2} - 2 i^{31} - 12 i^{70}$

Step 1.10

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

$7 + i^{2} - 2 i^{31} - 12 i^{70}$

Step 1.11

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

$7 - 1 - 2 i^{31} - 12 i^{70}$

Step 1.12

Rewrite $i^{31}$ as ${(i^{4})}^{7} (i^{2} \cdot i)$ .

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Step 1.12.1

Factor out $i^{28}$ .

$7 - 1 - 2 (i^{28} i^{3}) - 12 i^{70}$

Step 1.12.2

Rewrite $i^{28}$ as ${(i^{4})}^{7}$ .

$7 - 1 - 2 ({(i^{4})}^{7} i^{3}) - 12 i^{70}$

Step 1.12.3

Factor out $i^{2}$ .

$7 - 1 - 2 ({(i^{4})}^{7} (i^{2} \cdot i)) - 12 i^{70}$

Step 1.13

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

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Step 1.13.1

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

$7 - 1 - 2 ({({(i^{2})}^{2})}^{7} (i^{2} \cdot i)) - 12 i^{70}$

Step 1.13.2

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

$7 - 1 - 2 ({({(- 1)}^{2})}^{7} (i^{2} \cdot i)) - 12 i^{70}$

Step 1.13.3

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

$7 - 1 - 2 (1^{7} (i^{2} \cdot i)) - 12 i^{70}$

Step 1.14

One to any power is one.

$7 - 1 - 2 (1 (i^{2} \cdot i)) - 12 i^{70}$

Step 1.15

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

$7 - 1 - 2 (i^{2} \cdot i) - 12 i^{70}$

Step 1.16

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

$7 - 1 - 2 (- 1 \cdot i) - 12 i^{70}$

Step 1.17

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

$7 - 1 - 2 (- i) - 12 i^{70}$

Step 1.18

Multiply $- 1$ by $- 2$ .

$7 - 1 + 2 i - 12 i^{70}$

Step 1.19

Rewrite $i^{70}$ as ${(i^{4})}^{17} i^{2}$ .

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Step 1.19.1

Factor out $i^{68}$ .

$7 - 1 + 2 i - 12 (i^{68} i^{2})$

Step 1.19.2

Rewrite $i^{68}$ as ${(i^{4})}^{17}$ .

$7 - 1 + 2 i - 12 ({(i^{4})}^{17} i^{2})$

Step 1.20

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

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Step 1.20.1

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

$7 - 1 + 2 i - 12 ({({(i^{2})}^{2})}^{17} i^{2})$

Step 1.20.2

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

$7 - 1 + 2 i - 12 ({({(- 1)}^{2})}^{17} i^{2})$

Step 1.20.3

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

$7 - 1 + 2 i - 12 (1^{17} i^{2})$

Step 1.21

One to any power is one.

$7 - 1 + 2 i - 12 (1 i^{2})$

Step 1.22

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

$7 - 1 + 2 i - 12 i^{2}$

Step 1.23

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

$7 - 1 + 2 i - 12 \cdot - 1$

Step 1.24

Multiply $- 12$ by $- 1$ .

$7 - 1 + 2 i + 12$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Subtract $1$ from $7$ .

$6 + 2 i + 12$

Step 2.2

Add $6$ and $12$ .

$18 + 2 i$