Convert to Rectangular 2(cos(pi/4)+isin(pi/4))

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

Step 1

Simplify each term.

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

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

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

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

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

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

Step 2

Simplify terms.

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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