## preserves angle, conformal

Let $f(z)$ be a function from $D \subseteq \mathbb{C}$ into $\mathbb{C}$, which has continuous real derivatives, non-zero gradients and which preserves the angle $\frac{\pi}{2}$ between curves. Prove that $f$ is conformal.

I know to prove conformal that we can prove that it preserves angles or holomorphic and its derivative is everywhere non-zero on $D \subseteq \mathbb{C}$. However, I am not sure how to do this. I need some help on how to proceed. Thanks in advance.