Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$3 (\frac{1}{2} + i \sin (\frac{π}{3}))$

Step 1.2

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

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

Step 1.3

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

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

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Combine $3$ and $\frac{1}{2}$ .

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

Step 2.3

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

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