Question

Show the functions f= f(z); z=x+iy is nowhere differentiable

f(z)=cosy -i siny

how do i do this? heres my idea
separate them into u(x,y) and v(x,y) then differentiate them and since the first derivative of u(x,y) and v(x,y) does not equal i can deduce that they are nowhere differentiable?

hint on this question will be helpful. :)

Answer 1

That is correct. They have to satisfy the Cauchy-Riemann equations.

Answer 2

i see thanks :)