InterviewSolution
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InterviewSolution
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Let a be a complex number such that `|a| lt 1` and `z_(1),z_(2)…..` be vertices of a polygon such that `z_(k)=1+a+a^(2)+a^(3)+a^(k-1)`. Then, the vertices of the polygon lie within a circle.A. `|z-(1)/(1-a)|=(1)/(|a-1|)`B. `|z+(1)/(a+1)| = (1)/(|a+1|)`C. `|z-(1)/(1-a)|=|a-1|`D. `|z+(1)/(1-a)|=|a-1|` |
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Answer» Correct Answer - A Given, `z_(k) = 1 + a+ a^(2) +......+a^(k-1) = (1-a^(k))/(1-a)` `rArr a_(k) -(1)/(1-a) = - (a^(k))/(1-a)` `rArr |z_(k)-(1)/(1-a)|= (|a|^(k))/(|1-a|) lt (1)/(|1-a|)" " [because|a| lt 1]` Hence , `z_(k)` lies within the circle. `therefore |z-(1)/(1-a)|= (1)/(|1-a|)` |
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