InterviewSolution
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InterviewSolution
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If `z=x+iy (x, y in R, x !=-1/2)`, the number of values of z satisfying `|z|^n=z^2|z|^(n-2)+z |z|^(n-2)+1.` `(n in N, n>1)` is |
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Answer» Correct Answer - B The given equation is `|z|^(n)=(z^(2)+z)^(n-2+1)` `rArr z^(2)+z` is real `rArr z^(2)+z=barz^(2)+barz` `rArr (z-z)(z+barz+1)=0` `rArr z=barz=x " as " z+barz+1ne0(xne-1//2)` Hence, the given equation reduces to `x^(n)=x^(n)+x|x|^(n-2+1)` `rArr x|x|^(n-2)=-1` `rArr x=-1` So number of solution is 1. |
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