Find All Complex Number Solutions z=3(cos(pi/6)+isin(pi/6))

$z = 3 (\cos (\frac{π}{6}) + i \sin (\frac{π}{6}))$

Simplify each term.

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$z = 3 (\frac{\sqrt{3}}{2} + i \sin (\frac{π}{6}))$

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$z = 3 (\frac{\sqrt{3}}{2} + i \frac{1}{2})$

Combine $i$ and $\frac{1}{2}$ .

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

Simplify terms.

Apply the distributive property.

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

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

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

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

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