 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/7/solution

Evaluate the derivative along real and imaginary increments. For a holomorphic function, both give the same value:

f^{'} (z) = u_{x} + i v_{x} = \frac{u _{y} + i v _{y}}{i} = v_{y} - i u_{y} .

u_{x} = v_{y}, u_{y} = - v_{x} .

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