Thread: Using De Moivre's Theorem

Hello,
Doing a practice paper and found this question, not sure what to do:

Write down de Moivre's Theorem for n=5. hence show that for



where A, B, C are constants to be determined.
Deduce the limiting value of as tends to zero.

I've written de Moivre for n=5:



But don't know where to go from there, at all.

Thanks

Originally Posted by alexgeek

Hello,
Doing a practice paper and found this question, not sure what to do:


I've written de Moivre for n=5:



But don't know where to go from there, at all.

Thanks

From De'moivre's theorem it follows that

.

Now I suggest you expand the left hand side of this identity and equate the imaginary part of it to .

Finally got it, tried expanding it by hand then realised I could do it by binomial. Cheers