# Prove that z^(k+1) is true for n=k+1

• Oct 25th 2013, 06:40 AM
Darrylcwc
Prove that z^(k+1) is true for n=k+1
I'm having some problem recalling the trig identity.

I've work up till this part:

r^k . r^1 [Cos(k.theta)Cos(theta)-Sin(K.theta)Sin(theta)+i(Cos(theta)Sin(K.theta)+Co s(K.theta)Sin(theta)]

I need to reduce the above to its relevant trig identity to yield: r^(K+1) [Cos(K+1)theta + iSin(K+1)theta]

• Oct 26th 2013, 06:18 AM
MINOANMAN
Re: Prove that z^(k+1) is true for n=k+1
Hey Darrykwc
I believe you are trying to prove De Moivre's Theorem.
Find the proof here
De Moivre's formula - Wikipedia, the free encyclopedia
• Oct 26th 2013, 03:50 PM
Prove It
Re: Prove that z^(k+1) is true for n=k+1
Quote:

Originally Posted by Darrylcwc
I'm having some problem recalling the trig identity.

I've work up till this part:

r^k . r^1 [Cos(k.theta)Cos(theta)-Sin(K.theta)Sin(theta)+i(Cos(theta)Sin(K.theta)+Co s(K.theta)Sin(theta)]

I need to reduce the above to its relevant trig identity to yield: r^(K+1) [Cos(K+1)theta + iSin(K+1)theta]