Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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 1.2.2

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

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

Step 1.2.3

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

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

Step 1.3

One to any power is one.

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

Step 1.4

Multiply $5$ by $1$ .

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

Step 1.5

Factor out $i^{2}$ .

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

Step 1.6

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

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

Step 1.7

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

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

Step 1.8

Multiply $- 1$ by $6$ .

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

Step 1.9

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

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Step 1.9.1

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

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

Step 1.9.2

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

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

Step 1.9.3

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

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

Step 1.10

Multiply $2$ by $1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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

Step 2.2

Add $5 y$ and $2 y$ .

$- 2 x i + 7 y$