Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

$4 (\frac{1}{2} + i \frac{π}{3})$

Step 1.2

Combine $i$ and $\frac{π}{3}$ .

$4 (\frac{1}{2} + \frac{i π}{3})$

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$4 (\frac{1}{2}) + 4 \frac{i π}{3}$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $4$ .

$2 (2) \frac{1}{2} + 4 \frac{i π}{3}$

Step 2.2.2

Cancel the common factor.

$2 \cdot 2 \frac{1}{2} + 4 \frac{i π}{3}$

Step 2.2.3

Rewrite the expression.

$2 + 4 \frac{i π}{3}$

Step 2.3

Combine $4$ and $\frac{i π}{3}$ .

$2 + \frac{4 i π}{3}$