Solution
= Solution
Every <eigenvalue> of a <Hermitian matrix> is real: if $He=\lambda e$ with $e^\dagger e=1$, then $\lambda=e^\dagger He=\overline{e^\dagger He}$. Therefore
$$
\boxed{\operatorname{Im}(\lambda_1\lambda_2)=0.}
$$
= Solution
Every <eigenvalue> of a <Hermitian matrix> is real: if $He=\lambda e$ with $e^\dagger e=1$, then $\lambda=e^\dagger He=\overline{e^\dagger He}$. Therefore
$$
\boxed{\operatorname{Im}(\lambda_1\lambda_2)=0.}
$$