InterviewSolution
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InterviewSolution
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If `omega ` is the imaginary cube roots of unity, then the number of pair of integers (a,b) such that `|aomega + b| = 1` is ______. |
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Answer» Correct Answer - 6 We have `|aomega + b| = 1` `rArr |aomega + b|^(2) =1` `rArr (aomega + b)(abaromega +b) = 1` `rArr a^(2) + ab (omega + baromega) +b^(2) =1` `rArr a^(2) -ab + b^(2)=1` `rArr (a-b)^(2)+ab = 1" "(1)` When `(a-b)^(2) = 0` and ab = 1, `then (1,1),(-1,-1)` when `(a-b)^(2) = 1 and ab = 0`, then `(0,1),(1,0),(0,-1),(-1,0)` Hence, there are 6 ordered pairs. |
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