(I'm unsure as to whether this question can be regarded as calculus, however, I am currently studying Differential Calculus at university as a first year subject so, I just made the assumption there - this question came from my course's textbook.)
"Find all solutions of z^4 = 8 + 8√3i, and plot them in the complex plane."
First of all, I'm unsure with how you would be able to find the solutions for the equation. I understand that there are 4 roots to the equation, one is for linear equations in z and two for quadratics in z^2 and so on. I know that you need to express z^4 = 8 + 8√3i into the form r(cost + isint) and then use de Moivre's theorem from there. So, from doing that - how would you be able to get the points that need to be plotted? Although, I'm still confused as to how you would work out the entire question. This question was given as an example from my textbook however, I wasn't able to follow on with it quite clearly. What I am most particularly confused about is how you would plot the points. Apparently you can find one solution given that the other solutions of z^n = k form a regular polygon around the origin (which confuses me even more...) So, is anyone able to provide a helpful step-by-step procedure with how to get the answer?
Any help would be greatly appreciated. Thank you.