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## Homework Statement

Find the domain in which the complex-variable function ##f(z)=(z+1)Ln(z)## is differentiable. Note: ##Ln(z)## is the principal complex logarithmic function.

## Homework Equations

Cuachy-Riemann Equations?

## The Attempt at a Solution

The solution I have in mind would be to let ##z=x+iy## then substitute and simplify. Check if it satisfies the Cauchy-Riemann equations, the real and imaginary part of ##f## is continuous and their first-order partial derivative are continuous as well. But, I do not know how to simplify ##Arg(z)## in ##Ln(z)=Log_e(z)+iArg(z)## because ##z## is not fixed.