InterviewSolution
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InterviewSolution
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Suppose `A`is a complex number and `n in N ,`such that `A^n=(A+1)^n=1,`then the least value of `n`is`3`b. `6`c. `9`d. `12`A. 3B. 6C. 9D. 12 |
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Answer» Correct Answer - B Let `A=x+iy.`Given, `|A|=1rArrx^(2)+y^(2)=1` and `|A+1|=1rArr(x+1)^(2)+y^(2)=1` `rArr x=-(1)/(2)andy=pm(sqrt3)/(2)` `rArr A=omegaoromega^(2)` `rArr (omega)^(n)=(1+omega)^(n)=(-omega^(2))^(2)` Therefore, n must be even and divisible by 3. |
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