Find the principle argument Arg z when
z = (sqrt(3) - i)^6
The Attempt at a Solution
I'm sorry to say that I'm not sure how to solve this problem. It's my understanding that what this question is basically asking me to do is find theta such that
exp(i*theta*6) = (sqrt(3)-i)^6
However I'm not sure how to solve this.
cos(theta) = sqrt(3)
sin(theta) = -i
In order for sin(theta) = -1, then theta must be equal to -pi/2. However cos(-pi/2) =/= sqrt(3). I seem to not understand what this question is asking me exactly or how to solve this problem.
Thanks for any help.