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I'm reading a rather old mechanics paper and the author uses the following to derive certain stresses.

Let x + iy = f(u + iv)

Then, J$e^{i\phi}$ = f'(u+iv)

J is the Jacobian, and $\phi$ is the angle between a tangent to the curve v = constant and the x axis

given f is a conformal mapping.

How can this be derived?

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    i'm actually asking for a proof of $Je^{iϕ(u,v)}=f′(u+iv)$. f'() is the derivative with respect to a single complex variable z = u+iv.2011-04-05

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Dear Kunal Bhalla, probably the author of the paper is going to introduce just a notation. Given a conformal map $f$ let us denote by $J$ the modulus of f' and by $\phi$ its argument modulo $2\pi$.

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    Thanks—based on Brian's answer that's what I was thinking—I misread J to be the Jacobian and considered it to be the complex jacobian and just got stuck on that.2011-04-05