Obtain the representation of f (z) in terms of complex variable z. Find real part; u (x, y), and imaginary part; v (x, y), in cartesian coordinates. Employ De Moivre's formula to find the solution....

Extracted text: Obtain the representation of f (z) in terms of complex variable z. Find real part; u (x, y), and imaginary part; v (x, y), in cartesian coordinates. Employ De Moivre's formula to find the solution. Q22] A harmonic function; u (x, y) = Log (2² + y²) is given. Show that the function is harmonic. Compute harmonic conjugate; v (x, y) of this function. Q23] Evaluate the following mathematical operations. Compute only two values (k = 0, 1) of the operations in (a) and (e). Write your results in Cartesian form. %3D log (e? cos (3) + ie? sin (3)) b) cos ( T/2 +iLog (6)) c) cosh ( Log (4) – it/2) d) 18A e) (-e").