I have learnt that in a matrix, if there are complex eigenvalues, they should come as conjugate pairs. Also, I know that, in a diagonal matrix, eigenvalues are the diagonal elements.
So how about the following matrix?
$$\begin{pmatrix} i & 0\\ 0& 2 \end{pmatrix}$$
Shouldn't the eigenvalues be $i$ and $2$, where it doesn't have a conjugate pair?!
I appreciate your help to clarify my mistake.