Question

Show that the function f(z) = xy + iy is continuous everywhere but not differentiable anywhere. 

Answer 1

Given f(z) = xy + iy

u = xy, v = y

x and y are continuous functions ,therefore u and v are also continuous.

But u = xy, v = y

u_x = y, v_x = 0

u_y = x, v_y = 1

u_x ≠ v_y and v_x - u_y

C-R equations are not satisfied. 

Hence f(z) is not differentiable anywhere though it is continuous everywhere.