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prove-that-e-2y-1-e-2y-lt-tan-z-i-lt-e-2y-1-e-2y-y-gt-0-how-can-solve-this-




Question Number 138236 by mohammad17 last updated on 11/Apr/21
prove that     (e^(−2y) /(1+e^(−2y) ))<∣tan(z) − i∣<(e^(−2y) /(1−e^(−2y) ))   ,y>0    how can solve this ?
$${prove}\:{that}\: \\ $$$$ \\ $$$$\frac{{e}^{−\mathrm{2}{y}} }{\mathrm{1}+{e}^{−\mathrm{2}{y}} }<\mid{tan}\left({z}\right)\:−\:{i}\mid<\frac{{e}^{−\mathrm{2}{y}} }{\mathrm{1}−{e}^{−\mathrm{2}{y}} }\:\:\:,{y}>\mathrm{0} \\ $$$$ \\ $$$${how}\:{can}\:{solve}\:{this}\:? \\ $$
Commented by mr W last updated on 11/Apr/21
you can not compare two complex  numbers. do you mean ∣tan(z) − i∣?
$${you}\:{can}\:{not}\:{compare}\:{two}\:{complex} \\ $$$${numbers}.\:{do}\:{you}\:{mean}\:\mid{tan}\left({z}\right)\:−\:{i}\mid? \\ $$
Commented by mohammad17 last updated on 11/Apr/21
yes yes sory sir
$${yes}\:{yes}\:{sory}\:{sir} \\ $$
Commented by mohammad17 last updated on 11/Apr/21
can you solve this sir
$${can}\:{you}\:{solve}\:{this}\:{sir} \\ $$
Commented by mr W last updated on 11/Apr/21
with z=x+yi ?
$${with}\:{z}={x}+{yi}\:? \\ $$
Commented by mohammad17 last updated on 11/Apr/21
yes sir can you help me please
$${yes}\:{sir}\:{can}\:{you}\:{help}\:{me}\:{please} \\ $$

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