2. (a) Find all the analytic functions f = u + iv, where u is given...

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2. (a) Find all the analytic functions f = u + iv, where u is given as [3] u(r, y) = e" cos y + xy, (r, y) € R". %3D (b) Determine an upper bound of the value of the integration Log z dz, where C is the quarter unit circle centred at the origin, lying in the first quadrant and oriented in counterclockwise direction. [3] 2. (a) Find all the analytic functions f = u + iv, where u is given as [3] u(r, y) = e" cos y + xy, (r, y) € R". %3D (b) Determine an upper bound of the value of the integration Log z dz, where C is the quarter unit circle centred at the origin, lying in the first quadrant and oriented in counterclockwise direction. [3]