Aus Online Mathematik Brückenkurs 2

A polynomial equation which has real coefficients always has complex conjugate roots. We can therefore say directly that the equation, in addition to the roots \displaystyle z=2i and \displaystyle z=-1+i, has roots \displaystyle z=\overline{2i}=-2i and \displaystyle z=\overline{-1+i}=-1-i. Because the equation is of degree 4, it does not have more than 4 roots.

The answer is thus

\displaystyle z = \left\{\begin{align} &\phantom{+}2i\,,\\[5pt] &-2i\,,\\[5pt] &-1+i\,,\\[5pt] &-1-i\,\textrm{.} \end{align} \right.