1. The problem statement, all variables and given/known data Using f(z) = f(re^iθ) = R(r,θ)e^iΩ(r,θ), show that the Cauchy-Riemann conditions in polar coordinates become ∂R/∂r = (R/r)∂Ω/∂θ 2. Relevant equations Cauchy-Riemann in polar coordinates Hint: Set up the derivative first with dz radial and then with dz tangential 3. The attempt at a solution df/dz = (∂R/∂r)(∂r/∂z)e^iΩ + R(∂Ω/∂θ)(∂θ/∂z)e^iΩ Now, I have no idea what dz tangential should be. I'm guessing that I should set the radial df/dz equal to the tangential df/dz, but I have no idea about the tangential or if my radial is right. Functionals are confusing to me, and complex functionals even more so.