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December 3rd, 2016, 01:43 PM   #1
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Real and Imaginary parts

Hi guys, I'm really stuck on this question; if you could help, it would be really great, thanks.
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Last edited by skipjack; December 3rd, 2016 at 01:49 PM.
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December 3rd, 2016, 03:08 PM   #2
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(a) As $u - v$ is constant $\partial u/\partial x = \partial v/\partial x$ and $\partial u/\partial y = \partial v/\partial y$. As the Cauchy-Riemann equations also hold, it's easily deduced that all the partial derivatives are zero, which implies that $f$ is constant.

Can you now make progress with (b) by using the hint provided?
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