Let C be the boundary of the square with vertices 0, 1, 1+ i, and i with counterclockwise orientation. (1) Find a parameterisation for C. (2) Evaluate the integral [fa(z) dz, where fa(z) = x² − y² — ax and a is a complex constant. (3) Find all values of a such that So fal fa(z) dz = 0. (4) Let ao be one of the values found in (3). Can we conclude that fao is analytic inside of C? Explain your answer carefully.

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