Prove that the matrix $$ A = \begin{bmatrix}2+a & -1\\-1 & 2+a\end{bmatrix} $$ is positive definite in $\mathbb{C^2}$ for any $a > -1$
If the question had been posed to show positive definiteness in $\mathbb{R^2}$, I would have had no problem. However, I have never worked in the complex plane, and we have never really talked about it in class, so I'm grasping for ideas with no idea what I'm trying to do.