Algebra Examples

$10 i^{62} + 11 i^{41} + 6 i^{84} + 5 i^{104}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{62}$ as ${(i^{4})}^{15} i^{2}$ .

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Step 1.1.1

Factor out $i^{60}$ .

$10 (i^{60} i^{2}) + 11 i^{41} + 6 i^{84} + 5 i^{104}$

Step 1.1.2

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

$10 ({(i^{4})}^{15} i^{2}) + 11 i^{41} + 6 i^{84} + 5 i^{104}$

Step 1.2

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

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Step 1.2.1

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

$10 ({({(i^{2})}^{2})}^{15} i^{2}) + 11 i^{41} + 6 i^{84} + 5 i^{104}$

Step 1.2.2

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

$10 ({({(- 1)}^{2})}^{15} i^{2}) + 11 i^{41} + 6 i^{84} + 5 i^{104}$

Step 1.2.3

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

$10 (1^{15} i^{2}) + 11 i^{41} + 6 i^{84} + 5 i^{104}$

Step 1.3

One to any power is one.

$10 (1 i^{2}) + 11 i^{41} + 6 i^{84} + 5 i^{104}$

Step 1.4

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

$10 i^{2} + 11 i^{41} + 6 i^{84} + 5 i^{104}$

Step 1.5

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

$10 \cdot - 1 + 11 i^{41} + 6 i^{84} + 5 i^{104}$

Step 1.6

Multiply $10$ by $- 1$ .

$- 10 + 11 i^{41} + 6 i^{84} + 5 i^{104}$

Step 1.7

Rewrite $i^{41}$ as ${(i^{4})}^{10} i$ .

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Step 1.7.1

Factor out $i^{40}$ .

$- 10 + 11 (i^{40} i) + 6 i^{84} + 5 i^{104}$

Step 1.7.2

Rewrite $i^{40}$ as ${(i^{4})}^{10}$ .

$- 10 + 11 ({(i^{4})}^{10} i) + 6 i^{84} + 5 i^{104}$

Step 1.8

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

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Step 1.8.1

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

$- 10 + 11 ({({(i^{2})}^{2})}^{10} i) + 6 i^{84} + 5 i^{104}$

Step 1.8.2

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

$- 10 + 11 ({({(- 1)}^{2})}^{10} i) + 6 i^{84} + 5 i^{104}$

Step 1.8.3

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

$- 10 + 11 (1^{10} i) + 6 i^{84} + 5 i^{104}$

Step 1.9

One to any power is one.

$- 10 + 11 (1 i) + 6 i^{84} + 5 i^{104}$

Step 1.10

Multiply $i$ by $1$ .

$- 10 + 11 i + 6 i^{84} + 5 i^{104}$

Step 1.11

Rewrite $i^{84}$ as ${(i^{4})}^{21}$ .

$- 10 + 11 i + 6 {(i^{4})}^{21} + 5 i^{104}$

Step 1.12

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

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Step 1.12.1

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

$- 10 + 11 i + 6 {({(i^{2})}^{2})}^{21} + 5 i^{104}$

Step 1.12.2

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

$- 10 + 11 i + 6 {({(- 1)}^{2})}^{21} + 5 i^{104}$

Step 1.12.3

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

$- 10 + 11 i + 6 \cdot 1^{21} + 5 i^{104}$

Step 1.13

One to any power is one.

$- 10 + 11 i + 6 \cdot 1 + 5 i^{104}$

Step 1.14

Multiply $6$ by $1$ .

$- 10 + 11 i + 6 + 5 i^{104}$

Step 1.15

Rewrite $i^{104}$ as ${(i^{4})}^{26}$ .

$- 10 + 11 i + 6 + 5 {(i^{4})}^{26}$

Step 1.16

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

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Step 1.16.1

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

$- 10 + 11 i + 6 + 5 {({(i^{2})}^{2})}^{26}$

Step 1.16.2

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

$- 10 + 11 i + 6 + 5 {({(- 1)}^{2})}^{26}$

Step 1.16.3

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

$- 10 + 11 i + 6 + 5 \cdot 1^{26}$

Step 1.17

One to any power is one.

$- 10 + 11 i + 6 + 5 \cdot 1$

Step 1.18

Multiply $5$ by $1$ .

$- 10 + 11 i + 6 + 5$

Step 2

Simplify by adding numbers.

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Step 2.1

Add $- 10$ and $6$ .

$- 4 + 11 i + 5$

Step 2.2

Add $- 4$ and $5$ .

$1 + 11 i$