Assignment:
Let the function f(z) = u(x,y) + iv(x,y) be analytic in a domain D, and consider the families of level curves u(x,y) = c1 and v(x,y) = c2. Prove that these families are orthogonal. More precisely, show that if z0 = (x0, y0) is a point in D which is common to u(x,y) = c1 and v(x,y) = c2 and if f'(z0) doesn't equal 0, then the lines tangent to those curves at (x0, y0) are perpendicular.
Provide complete and step by step solution for the question and show calculations and use formulas.