Three Precalculus Problems to Check Answers

**Joanie** · March 18th 2009, 10:56 AM

3/18/09

I have done three problems and need verification of my answers.

1. Write the rectangular equation x=3 in polar form. My answer: rcostheta=3

2. Simplify {(sq. root of 3) + i}^4 My answer: 8 + 8(sq.root3i

3. Find (costheta+isintheta)^2 My answer: cos^2theta - isin^2theta

Thank you in advance for your help.

**Prove It** · March 18th 2009, 03:30 PM

Originally Posted by Joanie

3/18/09

I have done three problems and need verification of my answers.

1. Write the rectangular equation x=3 in polar form. My answer: rcostheta=3

2. Simplify {(sq. root of 3) + i}^4 My answer: 8 + 8(sq.root3i

3. Find (costheta+isintheta)^2 My answer: cos^2theta - isin^2theta

Thank you in advance for your help.

The first two are correct.

For the third

$(\cos{\theta} + i\sin{\theta})^2 = \cos^2{\theta} + 2i\cos{\theta}\sin{\theta} - \sin^2{\theta}$ .

Remember that

$\cos^2{\theta} - \sin^2{\theta} = \cos{2\theta}$ and $2\cos{\theta}\sin{\theta} = \sin{2\theta}$ .

So $(\cos{\theta} + i\sin{\theta})^2 = \cos{2\theta} + i\sin{2\theta}$ .

**Joanie** · March 18th 2009, 09:23 PM

Your comments were very helpful. Thanks so much.

Joanie

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