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How would u differentiate this function w.r.t. z - $$\frac{1}{z-2+3i}$$

U would need to split it and get partial derivatives right? Although im not sure how you'd split it into real and imaginary parts when the z and i are in the denominator?

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    Hint: For any complex number $z$, $$\frac{1}{z}=\frac{\bar z}{|z|^2}$$2012-04-18
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    The quotient rule works for complex differentiation just as well as for real differentiation.2012-04-18
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    If "differentiate" means $d/dz$, you use the same formulas as you do in real calculus. Writing "u" and "U" in your message could be confusing in a math forum, where single letters are usually variables. We have enough confusion from "a" and "I" already...2012-04-18
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    Try differentiating $f(z) = \frac{1}{z} = z^{-1}$ first (same rules as $\mathbb{R}$ differentiation), then use the composition rule with $g(z) = f(z-a)$, where $a = -2+3i$.2012-04-18

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