Here are the questions:
I have posted a link there to this topic, so the OP can see my work.Induction and Complex #'s. Calc help?
a) Prove, using mathematical induction, that for a positive integer n, (cos(x) + isinx)^n = cosnx +i sinnx where I^2 + -1
b)The complex number z is defined by z = cosx + isinx
I) show that 1/z = cos (-x) + isin(-x)
II) Deduce that z^n + z^-n = 2cosnx
c) Find the binomial expansion of (z + z^-1)^5
I) Hence show tat cos^5x = 1/16(acoas5x + bcos3x + ccosx) where a,b,c are positive integers to be found.
Thank you so much for you help!