InterviewSolution
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InterviewSolution
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`z_(1)`, `z_(2)` are two distinct points in complex plane such that `2|z_(1)|=3|z_(2)|` and `z in C` be any point `z=(2z_(1))/(3z_(2))+(3z_(2))/(2z_(1))` such thatA. `-1 le Re z le 1`B. `-2 le Re z le 2`C. `-3 le Re z le 3`D. None of these |
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Answer» Correct Answer - B `(b)` `z=(2z_(1))/(3z_(2))+(3z_(2))/(2z_(1))` `=(2)/(3)(|z_(1)|)/(|z_(2)|)e^(i(theta_(1)-theta_(2)))+(3)/(2)(|z_(2)|)/(|z_(1)|)e^(i(theta_(2)-theta_(1)))` `=e^(i(theta_(1)-theta_(2)))+e^(i(theta_(2)-theta_(1)))=2cos(theta_(1)-theta_(2))=2cosalpha` |
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