Determine the largest domain ohm

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1. Determine the largest domain Ω on which the function f(z) = log z / z is analytic, where log z is the principal branch of the logarithm. Furthermore, compute f'(z) on your domain Ω.

If u(x, y) = (1/2) ln(x² + y²) and v(x, y) = tan^-1 y/x, then is f(x + iy) = u(x, y) + iv(x, y) analytic on Ω, where Ω is the complex plane with the point z = 0 removed?

Reference no: EM131009554

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