Let . What are all possible solutions of:

So, after converting to polar form I have:

I have the answer which includes 7 solutions and I'm a little confused on how to get to them. I guess this is more a trig question?

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- August 22nd 2011, 09:56 AMterrorsquidSolution set using De Moivre's theorem
Let . What are all possible solutions of:

So, after converting to polar form I have:

I have the answer which includes 7 solutions and I'm a little confused on how to get to them. I guess this is more a trig question? - August 22nd 2011, 10:35 AMPlatoRe: Solution set using De Moivre's theorem
- August 22nd 2011, 11:19 AMOpalgRe: Solution set using De Moivre's theorem
- August 22nd 2011, 06:39 PMterrorsquidRe: Solution set using De Moivre's theorem
Hmm I still seem to be missing a step in my head. I don't understand how the k multiples of pi got inside the sin and cos functions. I can see that

can be written as

but from there I thought I just applied the power to the and then multiplied by which gives me:

What am I missing in between those steps? - August 22nd 2011, 10:09 PMSammySRe: Solution set using De Moivre's theorem
- August 22nd 2011, 10:15 PMProve ItRe: Solution set using De Moivre's theorem
- August 23rd 2011, 09:54 AMterrorsquidRe: Solution set using De Moivre's theorem
Ok, I think I get the process. My understanding is very superficial though. I only learned how to "apply the formula" and didn't cover what I am actually doing by solving one of these which is what I think my problem is.

Take a similar example:

. Find all the solutions for:

I convert to polar form:

I notice that so I figure there will be 4 solutions (not sure why).

I then apply the exponent 1/4 to get:

Then to get my solutions I just generate 4 answers by multiplying the exponent 1/4 by and adding it to cycling k from 0 - 3 to get:

I can see that it makes one revolution and the answers are recorded periodically and evenly depending on the denominator of the increments, and I seem to be able to generate the answers for these types of problems, I just feel awkward not knowing why I'm doing each step if you understand?

Will these problems always have a coefficient that can be expressed as an integer raised to a power so you can determine how many answers there should be? - August 23rd 2011, 10:32 AMPlatoRe: Solution set using De Moivre's theorem