Originally Posted by

**Beard** I have been asked to find all the solutios for the following equation

$\displaystyle z^4 = 128(-\sqrt{3} + i)$

and leave my answers in exponential form and then plot them on an argand diagram.

I think I could probably do it if the 128 wasn't there. If it isn't there I put

$\displaystyle (-\sqrt{3} + i)$ on an argand diagram and find that the argument or radius from the centre is 2. I think I can then change that to

$\displaystyle (-\sqrt{3} + i)^\frac{1}{4}$ becoming $\displaystyle 2e^{i\theta}$ or something along those lines.

Can anybody tell me how to put the 128 in and if I got the rest of it sort of correct? or if it is a trainwreck?