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How do i show that this function preserves angle? There is no function given along which this is mapped. I know that its derivative is $f'(z)=2z+1$ so it is conformal for all points except 1 and $z_0$ not equal to zero. But how do i show this preserves angle?

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1 Answer 1

An analytic function is conformal precisely where its derivative is non-$0$. Thus, conformality holds everywhere except at $z=-\frac12$.

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