(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Cauchy-Riemann Conditions in Polar Coordinates

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