# De Moivre's Theorem

#### vanalm

##### New member
I'm doing my homework and i keep getting a positive angle, but the answer is saying the angle is negative. why is this negative?

(3-i)^6

r=square root of 10

a=r cos alpha

alpha=3/square root of 10

alpha=18.43494882

I have done this and similar problems over and over and can't figure out how they get alpha= -18.43493882

#### pka

##### Elite Member
$$\displaystyle \L 3 - i = \sqrt {10} \left( {\cos (\theta ) + i\sin (\theta )} \right),\;\theta = \arctan \left( {\frac{-1}{{ 3}}} \right)$$

#### galactus

##### Super Moderator
Staff member
Because you have $$\displaystyle (3-i)$$

Coordinates (3,-1) are in the 4th quadrant.

$$\displaystyle tan^{-1}(\frac{-1}{3})=-18.43494882$$

$$\displaystyle (\sqrt{10})^{6}(-.352-i(.936))=-352-936i$$

#### vanalm

##### New member
thanks guys. i got it now.