I have to find the roots of this complex number.
$z^6-\frac{1-2i}{2-i}=0$
I simplified:
$z=\sqrt[6]{\frac{4}{5}-\frac{3}{5}i}$
Are the solutions these?
$z=\cos{\frac{\arctan{\frac{3}{4}}+2kπ}{6}+i\sin{\frac{\arctan{\frac{3}{4}}+2kπ}{6}}}$
(For k=0,1,2,3,4,5)