Complex Polar Forms, Sin and Cos Angles

**Problem:** Find all solutions of .

I can do the entire problem except for one part. After putting it into the correct form,

,

I do not know how to find the values of or . I know that is 8, but I can't figure out the values of cos and sin.

Any help is appreciated.

Re: Complex Polar Forms, Sin and Cos Angles

Quote:

Originally Posted by

**tangibleLime** **Problem:** Find all solutions of

.

I can do the entire problem except for one part. After putting it into the correct form,

,

I do not know how to find the values of

or

. I know that

is 8, but I can't figure out the values of cos and sin.

Any help is appreciated.

.

So, .

Equate real and imaginary terms to find .

Re: Complex Polar Forms, Sin and Cos Angles

Thanks,

So since , I need to equal -1 to satisfy the initial equation where . The only way to get -1 from is to have and to get rid of the imaginary number and return (-1 + i0).

Correct?

Re: Complex Polar Forms, Sin and Cos Angles

Quote:

Originally Posted by

**tangibleLime** Thanks,

So since

, I need

to equal -1 to satisfy the initial equation where

. The only way to get -1 from

is to have

and

to get rid of the imaginary number and return (-1 + i0).

Correct?

Yes. You should get three values of in the interval .

Re: Complex Polar Forms, Sin and Cos Angles

Quote:

Originally Posted by

**tangibleLime** **Problem:** Find all solutions of

.

Here is some notation:

So we can write

The cube roots of that is then