InterviewSolution
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InterviewSolution
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If `Z^5` is a non-real complex number, then find the minimum value of `(Imz^5)/(Im^5z)` |
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Answer» Correct Answer - `-4` Let z= a+ ib, `b ne 0` where Im Z = b `therefore " " Z^(5) = (a+ib)^(5)` `= a^(5) + 5a^(4) bi + 10^(3)b^(2)i^(2) + 10a^(2)b^(3)i^(2) + 5ab^(4)i^(4) + i^(5)b^(5)` `therefore" " Lm z^(5)=5a^(4)b- 10a^(2)b^(3) + b^(5)` `y= (ImZ^(5))/((ImZ^(5)))=((a)/(5))^(2)-10((a)/(b))^(2)+1` `= 5[((a)/(b))^(4)-2((a)/(b))^(2)+(1)/(5)]` `=5[(((a)/(b))^(2)-1)^(2) +(1)/(5)-1]` `=5(((a)/(b))^(2)-1)^(2)=4` So, `y_("min")= -4` |
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