Mathematics Tripos Papers

  • Part IA
  • Part IB
  • Part II
  • FAQ

1.I.3C

Complex Analysis or Complex Methods | Part IB, 2008

Given that f(z)f(z)f(z) is an analytic function, show that the mapping w=f(z)w=f(z)w=f(z)

(a) preserves angles between smooth curves intersecting at zzz if f′(z)≠0f^{\prime}(z) \neq 0f′(z)=0;

(b) has Jacobian given by ∣f′(z)∣2\left|f^{\prime}(z)\right|^{2}∣f′(z)∣2.

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