How do I find z using the theorem of De Moivre

I was going through some old work sheets and couldn't seem to do this one for some reason...

If find using the theorem of De Moivre.

What I did:

I assume I would find values for and and then I would be done right? Assuming this is what I am supposed to do, how do I solve for the angle ?

Thanks.

Re: How do I find z using the theorem of De Moivre

Quote:

Originally Posted by

**terrorsquid** I was going through some old work sheets and couldn't seem to do this one for some reason...

If

find

using the theorem of De Moivre.

Let

so

If then the two roots are

Re: How do I find z using the theorem of De Moivre

Quote:

Originally Posted by

**terrorsquid** I was going through some old work sheets and couldn't seem to do this one for some reason...

If

find

using the theorem of De Moivre.

What I did:

I assume I would find values for

and

and then I would be done right? Assuming this is what I am supposed to do, how do I solve for the angle

?

Thanks.

and .

So .

You have

You will need to use half angle identities to evaluate these exactly.

There is also another square root. You should know that square roots are evenly spaced about a circle, so these two square roots will have the same magnitude and are separated by an angle of , so the other square root is

and you should have those values from the first square root :)