Convert to Rectangular 3(cos(pi/4)+isin(pi/4))

$3 (\cos (\frac{π}{4}) + i \sin (\frac{π}{4}))$

Step 1

Simplify each term.

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

$3 (\frac{\sqrt{2}}{2} + i \sin (\frac{π}{4}))$

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

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

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

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

Step 2

Simplify terms.

Apply the distributive property.

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

Combine $3$ and $\frac{\sqrt{2}}{2}$ .

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

Combine $3$ and $\frac{i \sqrt{2}}{2}$ .

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