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Polar form of the Cauchy-Riemann equations is

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Cauchy-Riemann equations:

Rectangular form:

f(z) = u(x, y) + f v(x, y)

f(z) to be analytic it needs to satisfy Cauchy Riemann equations

ux = vy, uy = -vx

Polar form:

f(z) = u(r, θ) + f v(r, θ)

 and uθ = -rvr

​​

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