InterviewSolution
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InterviewSolution
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If `|z| =1 ` and `w=(z-1)/(z+1)` (where `z != -1`) then `Re(w)` is (A) 0 (B) `-1/|z+1|^2` (C) `|z/(z+1)| 1/|z+1|^2` (D) `sqrt2/|z+1|^2` |
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Answer» Correct Answer - A Since `|z| =1 and w = (z-1)/(z+1)` `rArr z-1 =wz+w rArr =(1+w)/(1-w)rArr |z|=(|1+w|)/(|1-w|)` `rArr |1-w|=|1+w| " "[ becaue |z|=1]` ltbr. On squaring both sides we get `1+ |w|^2-2|w| Re (w) =1 + |w|^2+2|w|Re (W)` [using `|z_1pm z_2|^2=|z_1|^2+|z_2|^2pm 2 |z_1||z_2| Re (bar z_1 z_2)]` `rArr 4 |w|Re |w|=0` `rArr " " Re (w)=0` |
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