I have problem in understanding the meaning of complex roots. If I have the following term: \begin{align} \lambda^2 = k^2 + i\frac{x}{y} \end{align} with $k$ being a complex number and $x,y\in \mathbb{R}_+$. I know that I now have two solutions, $-\lambda$ and $+\lambda$. But how do I compute them?
Somebody told me, that if I set Re$(\lambda)>0$, that this would define which of the two square roots is called $\lambda$ and which $-\lambda$. What does this mean?
Thank you for your help!
