Algebra Examples

$4 (\cos (\frac{7 π}{3}) + i \sin (\frac{7 π}{3}))$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$4 (\cos (\frac{π}{3}) + i \sin (\frac{7 π}{3}))$

Step 1.2

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

$4 (\frac{1}{2} + i \sin (\frac{7 π}{3}))$

Step 1.3

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$4 (\frac{1}{2} + i \sin (\frac{π}{3}))$

Step 1.4

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

$4 (\frac{1}{2} + i \frac{\sqrt{3}}{2})$

Step 1.5

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

$4 (\frac{1}{2} + \frac{i \sqrt{3}}{2})$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Apply the distributive property.

$4 (\frac{1}{2}) + 4 \frac{i \sqrt{3}}{2}$

Step 2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1

Factor $2$ out of $4$ .

$2 (2) \frac{1}{2} + 4 \frac{i \sqrt{3}}{2}$

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$2 + 4 \frac{i \sqrt{3}}{2}$

Step 2.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.1

Factor $2$ out of $4$ .

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

Step 2.3.2

Cancel the common factor.

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

Step 2.3.3

Rewrite the expression.

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

$2 + 2 i \sqrt{3}$