Algebra Examples

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

Step 1

Since $x = r \cos (θ)$ , replace $x$ with $r \cos (θ)$ .

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

Step 2

Simplify the right side.

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Step 2.1

Simplify $3 (\cos (\frac{π}{6}) + i \sin (\frac{π}{6}))$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

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

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

Step 2.1.1.2

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

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

Step 2.1.1.3

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

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

Step 2.1.2

Simplify terms.

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Step 2.1.2.1

Apply the distributive property.

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

Step 2.1.2.2

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

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

Step 2.1.2.3

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

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