InterviewSolution
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InterviewSolution
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Given `z`is a complex number with modulus 1. Then the equation `[(1+i a)//(1-i a)]^4=z`hasall roots real and distincttwo real and two imaginarythree roots two imaginaryone root real and three imaginaryA. all roots real and distinctB. two real and tw imaginaryC. three roots real and one imaginaryD. one root real and three imaginary |
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Answer» Correct Answer - A `((1+ia)/(1-ia))^(4) =z` or ` |(1+ia)/(1-ia)|^(4) = |z|` or `|(a-i)/(a+i)|^(4) = 1` ` or |a -i|= |a + i|` Therefore, a lies on the perpendicular bisector of iand -i. which is the real axis. Hence,all the roots are real.Obvioulsy roots are distinct. |
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