Convert to Rectangular 4(cos(300)+isin(300))

$4 (\cos (300) + i \sin (300))$

Step 1

Simplify each term.

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

$4 (\cos (60) + i \sin (300))$

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

$4 (\frac{1}{2} + i \sin (300))$

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.

$4 (\frac{1}{2} + i (- \sin (60)))$

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

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

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

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

Step 2

Simplify terms.

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{i \sqrt{3}}{2}$ into the numerator.

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

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 1$ by $2$ .

$2 - 2 i \sqrt{3}$

Convert to Rectangular 4(cos(300)+isin(300))

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