## complex number

1. The problem statement, all variables and given/known data
find the four fourth roots of -2$$\sqrt{3}$$+i2

i dont have any attempt for a solution because i dont know what to do..
im really lost.. i regret sleeping in class
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
 Recognitions: Gold Member Science Advisor Staff Emeritus I imagine you were intended to use DeMoivres' theorem: If a complex number can be written in polar form $z= r(cos(\theta)+ i sin(\theta))$ then its nth power, zn, can be written $z^n= r^n(cos(n\theta)+ i sin(n\theta)$ In your case, n is the fraction 1/4. Convert $-2\sqrt{3}+ 2i$ to polar form (which happens to be pretty simple). Take the real fourth root of r. Remember that you can add any multiple of $2\pi$ to $\theta$. Dividing by 1/4 will give you different results for different multiples of $2\pi$.
 im having some problem in the angle.. what i dis is this z=r cis (theta) x=-2(sqrt3) y=2 r=4 so theta=-60 then, will i just substitute the numbers to the equation?

Recognitions:
Gold Member
Yes, of course. r= 4 and theta= - 60 degrees (although I would prefer theta= -$\pi/3$).