# Math Help - DeMoivre's Theorem Problem

1. ## DeMoivre's Theorem Problem

Any Help will be Appreciated

DeMoivre's Theorem is this ( i is the imaginary unit):

(cos(x) + isin(x)) ^ n = con(nx) + isin(nx)

Let n = 3, and deduce the following

sin(3x) = 3 ((cos(x)) ^ 2) (sin(x)) - (sin(x) ^ 3)

and

cos(3x) = (cos(x) ^ 3) - 3 (cos(x)) (sin(x) ^ 2)

I can simplyify to the point where I need to use the other equation to prove the one I'm on. However, I can't use that unless I have already proved one of them first.

2. Originally Posted by hashshashin715
Any Help will be Appreciated

DeMoivre's Theorem is this ( i is the imaginary unit):

(cos(x) + isin(x)) ^ n = con(nx) + isin(nx)

Let n = 3, and deduce the following

sin(3x) = 3 ((cos(x)) ^ 2) (sin(x)) - (sin(x) ^ 3)

and

cos(3x) = (cos(x) ^ 3) - 3 (cos(x)) (sin(x) ^ 2)

I can simplyify to the point where I need to use the other equation to prove the one I'm on. However, I can't use that unless I have already proved one of them first.

Write $\left(\cos x + i\sin x\right)^3$ in two ways: first, using de Moivre theorem , and second using the binomial expansion $(a+b)^3=a^3+3a^2b+3ab^2+b^3$ (pay attention to the imaginary unit here!). Finally, just equal real and imaginar parts in both expressions.

Tonio

3. Ok, Thanks