Solve for z z=2(cos(30 degrees )+isin(30 degrees ))

$z = 2 (\cos (30 °) + i \sin (30 °))$

Step 1

Simplify each term.

The exact value of $\cos (30 °)$ is $\frac{\sqrt{3}}{2}$ .

$z = 2 (\frac{\sqrt{3}}{2} + i \sin (30 °))$

The exact value of $\sin (30 °)$ is $\frac{1}{2}$ .

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

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

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

Step 2

Simplify terms.

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$z = \sqrt{3} + i$