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Calculus and Beyond Homework Help
Where is ##(z+1)Ln(z)## differentiable?
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[QUOTE="Terrell, post: 6044501, member: 582739"] [h2]Homework Statement [/h2] 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. [h2]Homework Equations[/h2] Cuachy-Riemann Equations? [h2]The Attempt at a Solution[/h2] 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. [/QUOTE]
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Calculus and Beyond Homework Help
Where is ##(z+1)Ln(z)## differentiable?
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