Originally Posted by

**arbolis** I must find the roots of the following equation : $\displaystyle z^2-2i=0$ and graph them.

My attempt : $\displaystyle z^2-2i=0 \Leftrightarrow r^2e^{2i\theta}=2i \Rightarrow r^2=2 $ and $\displaystyle e^{2i\theta}=i$ (I don't trust the implication here) and I don't reach anything.

Another attempt : $\displaystyle z^2-2i=0 \Leftrightarrow a^2-b^2+i(2ab)=2i \Rightarrow a=b=1 \Rightarrow z=1+i$ (easy to graph).

I notice that $\displaystyle |z|=\sqrt 2$ in my both attempts.

So what are the roots? I didn't know an equation could have roots!