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I've used the Cauchy-Riemann equations to find the analytic function:

$$y^2 - x^2 -2y + 2 + i(2x(1-y))$$

But I'm having a slight rearranging problem and need to write it in terms of $z$, where $z = x + iy$.

Any suggestions would be much appreciated

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4 
This is probably better suited for math.stackexchange.com. Further, this sounds alot like homework? – Michael Kissner May 22 2011 at 11:31

closed as too localized by Qiaochu Yuan, Dan Petersen, Nate Eldredge, Daniel Moskovich, Gerald Edgar May 22 2011 at 12:45

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