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

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

Simplify each term.

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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 $\frac{\sqrt{2}}{2}$ .

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

Apply the distributive property.

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

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

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Multiply $- 1$ by $5$ .

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

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

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

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

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Multiply $- 1$ by $5$ .

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

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

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

Simplify each term.

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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 Form 5(cos(225)+isin(225))

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