Question

Q.N0.2: Show that u(x,y)=ln(x^2 + y^2) and v(x,y)=2tan^-1(y/x) satisfy Cauchy-Riemann equations

(∂u/∂x)=(∂v/∂y) and (∂u/∂y)=(-∂v/∂x)

Answer 1

just crank it out

∂u/∂x = 2x/(x^2+y^2)
∂u/∂y = 2y/(x^2+y^2

∂v/∂x = -2y/(x^2+y^2)
∂v/∂y = 2x/(x^2+y^2