# Demoivre's Theorem: Am I doing it right?

1. Mar 3, 2007

### pugfug90

1. The problem statement, all variables and given/known data
Use Demoivre's Theorem to evaluate w^2, if w=3(cos30degs+ising30degs)
PS, it's really pi/6, but I converted it to 30 degrees since I can't write on the screen..

2. Relevant equations
z^n=r^n(cos n*theta + i sin n*theta)

3. The attempt at a solution

w^2=3^2 (cos 2*30degs + i sin 2*30degs_
w^2=9(cos60degs+isin60degs)
w^2=9(0.5+i [square root of 3]/2)
w^2=(9/2)+9i[square root of 3]/2

===
I copied the test review answer key.. but I'm not sure if I copied it down right..
The answer that I copied down was
9[square root of 3]/2 + i9[square root of 3]/2..

That answer would like like it would come from a 45deg thing.. but sinn and cosn are 60degs..

Just making sure.. So has anyone seen where I went wrong?

Last edited: Mar 3, 2007
2. Mar 3, 2007

### theperthvan

looks to be copied down wrong.
Just don't use decimals, write 9/2, not 4.5

3. Mar 3, 2007

### pugfug90

I edited my initial post since I forgot the imaginary "i" part. And yes, I realize that 9/2 is 4.5. Anyone else NOT get 4.5[square root of 3] as opposed to just plain old 4.5 (9/2) for the "real" part?

4. Mar 4, 2007

### cristo

Staff Emeritus
You copied the answers down incorrectly. The correct answer is $$w^2=\frac{9}{2}+i\frac{9\sqrt{3}}{2}$$.

5. Mar 4, 2007

Thanks!
:-)