Convert to Rectangular 5(cos(225)+isin(225))

$5 (\cos (225) + i \sin (225))$

Step 1

Simplify each term.

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

$5 (- \cos (45) + i \sin (225))$

The exact value of $\cos (45)$ is $\frac{\sqrt{2}}{2}$ .

$5 (- \frac{\sqrt{2}}{2} + i \sin (225))$

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 third quadrant.

$5 (- \frac{\sqrt{2}}{2} + i (- \sin (45)))$

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$5 (- \frac{\sqrt{2}}{2} + i (- \frac{\sqrt{2}}{2}))$

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

$5 (- \frac{\sqrt{2}}{2} - \frac{i \sqrt{2}}{2})$

Step 2

Apply the distributive property.

$5 (- \frac{\sqrt{2}}{2}) + 5 (- \frac{i \sqrt{2}}{2})$

Step 3

Multiply $5 (- \frac{\sqrt{2}}{2})$ .

Multiply $- 1$ by $5$ .

$- 5 \frac{\sqrt{2}}{2} + 5 (- \frac{i \sqrt{2}}{2})$

Combine $- 5$ and $\frac{\sqrt{2}}{2}$ .

$\frac{- 5 \sqrt{2}}{2} + 5 (- \frac{i \sqrt{2}}{2})$

Step 4

Multiply $5 (- \frac{i \sqrt{2}}{2})$ .

Multiply $- 1$ by $5$ .

$\frac{- 5 \sqrt{2}}{2} - 5 \frac{i \sqrt{2}}{2}$

Combine $- 5$ and $\frac{i \sqrt{2}}{2}$ .

$\frac{- 5 \sqrt{2}}{2} + \frac{- 5 (i \sqrt{2})}{2}$

Step 5

Simplify each term.

Move the negative in front of the fraction.

$- \frac{(5) \sqrt{2}}{2} + \frac{- 5 (i \sqrt{2})}{2}$

Move the negative in front of the fraction.

$- \frac{5 \sqrt{2}}{2} - \frac{5 i \sqrt{2}}{2}$

Convert to Rectangular 5(cos(225)+isin(225))

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