InterviewSolution
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InterviewSolution
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If `z!=1`and `(z^2)/(z-1)`is real, then the pointrepresented by the complex number z lies(1)either on thereal axis or on a circle passing through the origin(2)on a circle withcentre at the origin(3)either on thereal axis or on a circle not passing through the origin(4)on the imaginaryaxisA. either on the real axis or on a circle passing thorugh the origin.B. on a circle with centre at the origin.C. either on the real axis or an a circle not possing through the origin .D. on the imaginary axis . |
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Answer» Correct Answer - A `(z^(2))/(z-1) ` is purely real lt `therefore (z^(2))/(z-1) = (barz^(2))/(barz-1)` ` rArr zbarzz - z^(2) = zbarzbar - barz^(-2)` `rArr (z-barz) (|z|^(2) -( z+ barz))= 0` Either `z = barz` `rArr ` z lies on real axis. or `|z|^(2) = z+z` `rArr zbarz - z - barz = 0` `rArr x^(2) + y^(2) -2x = 0` Which represents a cricle passing throught origin. |
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