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Two functions, u(x,y) and v(x,y), are said to verify the Cauchy-Riemann differentiation equations if they satisfy...

Two functions, u(x,y) and v(x,y), are said to verify the Cauchy-Riemann

differentiation equations if they satisfy the following equations ∂u\dx=∂v/dy and ∂u/dy=−(∂v/dx)

a. Verify that the Cauchy-Riemann differentiation equations can be written in the polar coordinate form as

∂u/dr=1/dr ∂v/dθ and ∂v/dr =−1/r ∂u/∂θ

b. Show that the following functions satisfy the Cauchy-Riemann differen- tiation equations

u=ln sqrt(x^(2)+y^(2)) and v= arctan y/x.

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