Is the integral ∫z* dz from the point (0,0) to (3,2) on the complex plane path dependent?
I = ∫ f(z)dz = ∫udx - vdy + i ∫ vdx + udy
z = x-iy, u = x, v = -y
The Attempt at a Solution
I have no idea how to start. The methods given in the book and from real line integrals don't seem to apply here. For example the book recommends, for real line integrals, to substitute y = x so that it reduces to a single integral. For complex integrals, it is recommended to parameterize f(z) into a f(z(t)) and reduce it to a single integration.
I've tried z = re^iθ, so dz = r*i*e^iθ dθ + e^iθ dr, now how do I reduce this to a single integration?