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