InterviewSolution
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InterviewSolution
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If `z=x+iy` and `w=(1-iz)/(z-i)`, then `|w|=1` implies that in the complex plane(A)`z` lies on imaginary axis (B) `z` lies on real axis (C)`z` lies on unit circle (D) None of theseA. z lies on the imaginary axisB. z lies on the real axisC. z lies on the unit circleD. None of these |
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Answer» Correct Answer - B Since `|w| =1 rArr |(1-iz)/(z-i)|=1` `rArr |z-i|=|1-iz|` `rArr |z-i|=|z+i| [ therefore |1-iz|=|-i||z+i|=|z+i|]` `therefore` It is a perpendicular bisector of (0,1) i.e. X-axis .Thus z lies on the real axis |
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