Complex roots and roots of unity
\[z^{5}=((-\frac{1}{2})\sqrt{2})+((-\frac{1}{2})\sqrt{2})i\]
List all distinct roots as \(R\operatorname{cis}(\Theta_j\pi)\). Use the common positive radius R and coefficients \(0\le\Theta_j<2\) in strictly increasing order, starting at j=0. Also give the distinct count D and common multiplicity M