InterviewSolution
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InterviewSolution
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Let `O`, `A`, `B` be three collinear points such that `OA.OB=1`. If `O` and `B` represent the complex numbers `O` and `z`, then `A` representsA. `(1)/(barz)`B. `(1)/(z)`C. `barz`D. `z^(2)` |
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Answer» Correct Answer - A `(a)` Let `A` represents `z_(1)`. Since `OA.OB=1 :. |z_(1)-0|.|z-0|=1` `implies |z_(2)|=(1)/(|z|)` Also, `arg((z_(1)-0)/(z-0))=0impliesarg((z_(1))/(z))=0` `impliesargz_(1)=argz` If `theta` is the argument of `z`, then `z=|z|e^(itheta)` `:. z_(1)=(1)/(|z|)e^(etheta)=(1)/(|z|^(2))|z|e^(itheta)-(z)/(zbarz)=(1)/(barz)` `:. A` is `(1)/(baraz)` |
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