I've been researching complex analysis recently and come across a couple of questions that I'm a little confused about. This is one of them.
Let $u:U\to \mathbb R$ be a harmonic function on an open subset of $\mathbb C$. Show $v$ is a harmonic conjugate of u if and only if $u$ is a harmonic conjugate of $-v$.
I know I need to apply the Cauchy-Riemann equations but I'm a bit stuck on the logic of the problem, since if a function satisfies Cauchy-Riemann, it is not necessarily holomorphic is it?