Complex variables: f(z) = z Im(z^2)?
If f(z) = z Im(z^2), determine the points in the complex plane such that f is differentiable.
f(z) = z Im (z^2) = (x+iy) (2xy) = 2(x^2)y + 2x(y^2)i
determine the points in the complex plane such that f is differentiable.
df/dx=2xy+2y(x+iy), so i*df/dx=2ixy+2iy(x+iy)
And df/dy=2ixy+3x(x+iy)
This tell us f(z) is differentiable when x=iy.
is it right?