Algebra Examples

$9 (\cos (300) + i \sin (300))$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$9 (\cos (60) + i \sin (300))$

Step 1.2

The exact value of $\cos (60)$ is $\frac{1}{2}$ .

$9 (\frac{1}{2} + i \sin (300))$

Step 1.3

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.

$9 (\frac{1}{2} + i (- \sin (60)))$

Step 1.4

The exact value of $\sin (60)$ is $\frac{\sqrt{3}}{2}$ .

$9 (\frac{1}{2} + i (- \frac{\sqrt{3}}{2}))$

Step 1.5

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

$9 (\frac{1}{2} - \frac{i \sqrt{3}}{2})$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Apply the distributive property.

$9 (\frac{1}{2}) + 9 (- \frac{i \sqrt{3}}{2})$

Step 2.2

Combine $9$ and $\frac{1}{2}$ .

$\frac{9}{2} + 9 (- \frac{i \sqrt{3}}{2})$

Step 3

Multiply $9 (- \frac{i \sqrt{3}}{2})$ .

Tap for more steps...

Step 3.1

Multiply $- 1$ by $9$ .

$\frac{9}{2} - 9 \frac{i \sqrt{3}}{2}$

Step 3.2

Combine $- 9$ and $\frac{i \sqrt{3}}{2}$ .

$\frac{9}{2} + \frac{- 9 (i \sqrt{3})}{2}$

Step 4

Move the negative in front of the fraction.

$\frac{9}{2} - \frac{9 i \sqrt{3}}{2}$