prove-d-dz-tan-1-z-1-1-z-2-in-complex-number-help-me-sir-

Question Number 142729 by mohammad17 last updated on 04/Jun/21

p r o v e : \frac{d}{d z} ({t a n}^{- 1} z) = \frac{1}{1 + z^{2}} i n c o m p l e x n u m b e r

h e l p m e s i r

Answered by mathmax by abdo last updated on 06/Jun/21

same definition of differentiality

\frac{d}{dz} (arctanz) = \lim_{h \to 0} \frac{\arctan (z + h) - arctanz}{h}

=_{hospital} = \lim_{h \to 0} \frac{1}{1 + {(z + h)}^{2}} = \frac{1}{1 + z^{2}}