Unformatted text preview: f maps a point ( x, y ) to the point ( x + x , y + y ). Thus f is a translation by ( x , y ). 37 We have φ + iψ = U ◦ f + iV ◦ f = g ² ³´ µ ( U + iV ) ◦ f. Since V is a harmonic conjugate of U , U + iV is analytic. Thus g ◦ f is analytic, being the composition of two analytic functions. Hence φ + iψ is analytic and so ψ is a harmonic conjugate of φ ....
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- Fall '11
- Analytic function, Holomorphic function, Harmonic conjugate, Conformal mappings