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.