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Starting-from-substituting-z-x-iy-Identify-the-maximal-region-within-which-f-z-is-analytic-f-z-1-z-z-1-Note-Do-not-start-by-just-differentiating-f-z-Start-by-doing-a-substitution-of-x-




Question Number 201683 by aurpeyz last updated on 10/Dec/23
Starting from substituting z=x+iy. Identify  the maximal region within which f(z) is analytic  f(z)=(1/(z(z+1))).     Note. Do not start by just differentiating f(z).   Start by  doing a substitution of x and iy and   then verify Cauchy Rieman theorem.
$${Starting}\:{from}\:{substituting}\:{z}={x}+{iy}.\:{Identify} \\ $$$${the}\:{maximal}\:{region}\:{within}\:{which}\:{f}\left({z}\right)\:{is}\:{analytic} \\ $$$${f}\left({z}\right)=\frac{\mathrm{1}}{{z}\left({z}+\mathrm{1}\right)}.\: \\ $$$$ \\ $$$${Note}.\:{Do}\:{not}\:{start}\:{by}\:{just}\:{differentiating}\:{f}\left({z}\right).\: \\ $$$${Start}\:{by}\:\:{doing}\:{a}\:{substitution}\:{of}\:{x}\:{and}\:{iy}\:{and}\: \\ $$$${then}\:{verify}\:{Cauchy}\:{Rieman}\:{theorem}. \\ $$$$ \\ $$
Commented by aurpeyz last updated on 10/Dec/23
pls help
$${pls}\:{help} \\ $$

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