Question

If f(z) = u + iv is a regular function of z in a domain D the following relations hold in D

(d/dx|f(z)|)² + (d/dy|f(z)|)² = |f'(z)|²

Answer 1

(d/dx|f(z)|)² + (d/dy|f(z)|)² = |f'(z)|²

Let f(z) = u + iv is an analytic function