Let $\displaystyle f(z)$ be a function from $\displaystyle D \subseteq \mathbb{C}$ into $\displaystyle \mathbb{C}$, which has continuous real derivatives, non-zero gradients and which preserves the angle $\displaystyle \frac{\pi}{2}$ between curves. Prove that $\displaystyle f$ 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 $\displaystyle D \subseteq \mathbb{C}$. However, I am not sure how to do this. I need some help on how to proceed. Thanks in advance.