= Solution
A <conformal map> preserves local oriented angles and has a nonzero local <Geometric scale factor>[scale factor]. For an orientation-preserving complex map this is equivalent to <holomorphy> with $f'(z)\ne0$ at the point concerned. Infinitesimal figures are rotated and uniformly scaled there, but finite shapes need not be preserved: <derivative> magnitude and direction can vary across a region. <Antiholomorphic map>[Antiholomorphic maps] preserve unoriented angles while reversing orientation; the convention being used must be stated.
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