Complex NumbersHard
Question
Let ω be a complex cube root of unity with ω ≠ 1. fair die is thrown three times. If r1, r2 and r3 are the numbers obtained on the die, then the probability that ωr1 + ωr2 + ωr3 = 0 is
Options
A.1 / 18
B.1 / 9
C.2 / 9
D.1 / 36
Solution
r1, r2, r3 ∈ {1, 2, 3, 4, 5, 6}
r1, r2, r3 are of the form 3k, 3k + 1, 3k + 2
Required probability =
r1, r2, r3 are of the form 3k, 3k + 1, 3k + 2
Required probability =
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