InterviewSolution
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InterviewSolution
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Find the number of roots of the equation `z^(15) = 1` satisfying `|arg z| lt pi//2`. |
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Answer» Correct Answer - 7 We have `z^(15) = 1` `z=1^(1)/(15) = e^(i(2rpi)/(15)), r = 0, 1,2,.....,14` or `z =e^(pmi(2rpi)/(15)) , r=0,1,2,....7` The complex numbers having their arguments between `-(pi)/(2)` and `(pi)/(2)` are `e^(0), e^(pmi(2pi)/(15)),e^(pmi(4pi)/(15)),e^(pmi(6pi)/(15))`. Hence number of solutions is7. |
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