InterviewSolution
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InterviewSolution
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Let `|z|=2a n dw-(z+1)/(z-1),w h e r ez ,w , in C`(where `C`is the set of complex numbers). Then product of least and greatestvalue of modulus of `w`is__________. |
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Answer» Correct Answer - 1 Let `z = a+ib` Given `|z| = 2` `rArr a^(2) + b^(2) = 4 rArr a,b in [-2,2]` Now `w ((a+1)+ib)/((a-1)+ib),` `rArr |w| = sqrt(((a+i)^(2) + b^(2))/((a-1)^(2) + b^(2)))=sqrt((a^(2) + b^(2)+2a+1)/(a^(2) +b^(2) -2a+1)) = sqrt((5+2a)/(5-2a))` `|w|_("min") = sqrt((5+4)/(1)) = 3` (when a =2) `|w|_("min") = sqrt((5-4)/(9)) = (1)/(3)` (when a = -2) Hence, required product is 1. |
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