Convert to Rectangular 6(cos((9pi)/4)+isin((9pi)/4))

$6 (\cos (\frac{9 π}{4}) + i \sin (\frac{9 π}{4}))$

Step 1

Simplify each term.

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$6 (\cos (\frac{π}{4}) + i \sin (\frac{9 π}{4}))$

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$6 (\frac{\sqrt{2}}{2} + i \sin (\frac{9 π}{4}))$

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$6 (\frac{\sqrt{2}}{2} + i \sin (\frac{π}{4}))$

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$6 (\frac{\sqrt{2}}{2} + i \frac{\sqrt{2}}{2})$

Combine $i$ and $\frac{\sqrt{2}}{2}$ .

$6 (\frac{\sqrt{2}}{2} + \frac{i \sqrt{2}}{2})$

Step 2

Simplify terms.

Apply the distributive property.

$6 \frac{\sqrt{2}}{2} + 6 \frac{i \sqrt{2}}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$2 (3) \frac{\sqrt{2}}{2} + 6 \frac{i \sqrt{2}}{2}$

Cancel the common factor.

$2 \cdot 3 \frac{\sqrt{2}}{2} + 6 \frac{i \sqrt{2}}{2}$

Rewrite the expression.

$3 \sqrt{2} + 6 \frac{i \sqrt{2}}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$3 \sqrt{2} + 2 (3) \frac{i \sqrt{2}}{2}$

Cancel the common factor.

$3 \sqrt{2} + 2 \cdot 3 \frac{i \sqrt{2}}{2}$

Rewrite the expression.

$3 \sqrt{2} + 3 (i \sqrt{2})$

$3 \sqrt{2} + 3 i \sqrt{2}$