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.


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Question Number 201683 by aurpeyz last updated on 10/Dec/23

$S t a r t i n g f r o m s u b s t i t u t i n g z = x + i y . I d e n t i f y$ $t h e m a x i m a l r e g i o n w i t h i n w h i c h f (z) i s a n a l y t i c$ $f (z) = \frac{1}{z (z + 1)} .$ $N o t e . D o n o t s t a r t b y j u s t d i f f e r e n t i a t i n g f (z) .$ $S t a r t b y d o i n g a s u b s t i t u t i o n o f x a n d i y a n d$ $t h e n v e r i f y C a u c h y R i e m a n t h e o r e m .$
Commented by aurpeyz last updated on 10/Dec/23

$p l s h e l p$
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