Convert to Rectangular 7(cos((11pi)/6)+isin((11pi)/6))

$7 (\cos (\frac{11 π}{6}) + i \sin (\frac{11 π}{6}))$

Step 1

Simplify each term.

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

$7 (\cos (\frac{π}{6}) + i \sin (\frac{11 π}{6}))$

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

$7 (\frac{\sqrt{3}}{2} + i \sin (\frac{11 π}{6}))$

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.

$7 (\frac{\sqrt{3}}{2} + i (- \sin (\frac{π}{6})))$

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

$7 (\frac{\sqrt{3}}{2} + i (- \frac{1}{2}))$

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

$7 (\frac{\sqrt{3}}{2} - \frac{i}{2})$

Step 2

Simplify terms.

Apply the distributive property.

$7 \frac{\sqrt{3}}{2} + 7 (- \frac{i}{2})$

Combine $7$ and $\frac{\sqrt{3}}{2}$ .

$\frac{7 \sqrt{3}}{2} + 7 (- \frac{i}{2})$

Step 3

Multiply $7 (- \frac{i}{2})$ .

Multiply $- 1$ by $7$ .

$\frac{7 \sqrt{3}}{2} - 7 \frac{i}{2}$

Combine $- 7$ and $\frac{i}{2}$ .

$\frac{7 \sqrt{3}}{2} + \frac{- 7 i}{2}$

Step 4

Move the negative in front of the fraction.

$\frac{7 \sqrt{3}}{2} - \frac{7 i}{2}$

Convert to Rectangular 7(cos((11pi)/6)+isin((11pi)/6))

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