Suppose f(z) = u(r, θ)+iv(r, θ) is analytic in a domainD not containing the origin. Use th...

Suppose f(z) = u(r, θ)+iv(r, θ) is analytic in a domainD not containing the origin. Use the Cauchy-Riemann equations (2) in the form rur = vθ and rvr = −uθ to show that u(r, θ) satisfies Laplace’s equation in polar coordinates:

 (1)

 (2)