Q4] A complex function in term of polar coordinates, (r,0) is described as f(z) =u(r,0)+j v(r, ). The Cauchy-Riemann equations in polar coordinates are ди 1 dv dv 1 ди ar r d0 Or r d0 And the Laplace...

Extracted text: Q4] A complex function in term of polar coordinates, (r,0) is described as f(z) =u(r,0)+j v(r, ). The Cauchy-Riemann equations in polar coordinates are ди 1 dv dv 1 ди ar r d0 Or r d0 And the Laplace equation in polar equation in polar coordinates is a20. 100 r or' r2 a02 1 a20 By employing these equations, show that Ø(r,0)=r°cos(20) is harmonic and obtain harmonic conjugate, v(r,0) of u(r,0). The auxiliary of the harmonic conjugate is v (0,0) =0.