(a) find all points where the function f(z) = (x^2+y^2-2y)+i(2x-2xy) is differentiable, and compute the derivative at those points.

f is not complex-differentiable

Step-by-step explanation:

Let the functions u, v defined as follow

then f can be rewritten as

In order for f to be complex-differentiable in a point z=x+iy, it must satisfy the Cauchy-Riemann equations

But

and

As f does not satisfy the Cauchy-Riemann equations, f is not complex-differentiable.

17.08

correct me if i am wrong.