Q 3: Prove the Cauchy-Riemann relation. Show whether the function is analytic. $f(z) = 2xy + i(x^2 - y^2)$
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Step 1: The Cauchy-Riemann equations are given by: \[ \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} \] \[ \frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x} \] where \( f(z) = u(x, y) + iv(x, y) \). Show more…
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