 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-1/7/a/solution

For

f = u + i v

analytic in

z = x + i y

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

They follow by computing the same complex derivative along the real and imaginary coordinate directions.

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