Trigonometry Examples

$4 x i + 5 y i^{8} + 6 x i^{3} + 2 y i^{4}$

Step 1

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

$4 x i + 5 y {(i^{4})}^{2} + 6 x i^{3} + 2 y i^{4}$

Step 2

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

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Step 2.1

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

$4 x i + 5 y {({(i^{2})}^{2})}^{2} + 6 x i^{3} + 2 y i^{4}$

Step 2.2

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

$4 x i + 5 y {({(- 1)}^{2})}^{2} + 6 x i^{3} + 2 y i^{4}$

Step 2.3

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

$4 x i + 5 y \cdot 1^{2} + 6 x i^{3} + 2 y i^{4}$

Step 3

One to any power is one.

$4 x i + 5 y \cdot 1 + 6 x i^{3} + 2 y i^{4}$

Step 4

Multiply $5$ by $1$ .

$4 x i + 5 y + 6 x i^{3} + 2 y i^{4}$

Step 5

Rewrite $i^{3}$ as $i^{2} \cdot i$ .

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Step 5.1

Factor out $i^{2}$ .

$4 x i + 5 y + 6 x (i^{2} i) + 2 y i^{4}$

Step 5.2

Add multiplication sign between $i$ and $i^{2}$ .

$4 x i + 5 y + 6 x (i^{2} \cdot i) + 2 y i^{4}$

Step 6

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

$4 x i + 5 y + 6 x (- 1 i) + 2 y i^{4}$

Step 7

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

$4 x i + 5 y + 6 x (- i) + 2 y i^{4}$

Step 8

Multiply $- 1$ by $6$ .

$4 x i + 5 y - 6 x i + 2 y i^{4}$

Step 9

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

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Step 9.1

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

$4 x i + 5 y - 6 x i + 2 y {(i^{2})}^{2}$

Step 9.2

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

$4 x i + 5 y - 6 x i + 2 y {(- 1)}^{2}$

Step 9.3

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

$4 x i + 5 y - 6 x i + 2 y \cdot 1$

Step 10

Multiply $2$ by $1$ .

$4 x i + 5 y - 6 x i + 2 y$

Step 11

Subtract $6 x i$ from $4 x i$ .

$- 2 x i + 5 y + 2 y$

Step 12

Add $5 y$ and $2 y$ .

$- 2 x i + 7 y$

Step 13

Factor $- 1$ out of $- 2 x i + 7 y$ .

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Step 13.1

Factor $- 1$ out of $- 2 x i$ .

$- (2 x i) + 7 y$

Step 13.2

Factor $- 1$ out of $7 y$ .

$- (2 x i) - (- 7 y)$

Step 13.3

Factor $- 1$ out of $- (2 x i) - (- 7 y)$ .

$- (2 x i - 7 y)$