Complex NumbersEasy
Question
If the cube roots of unity are 1, ω, ω2 then the roots of the equation (x - 1)3 + 8 = 0, are
Options
A.- 1, - 1 + 2ω, - 1 - 2ω2
B.-1, -1, - 1
C.-1, 1 - 2ω, 1 - 2ω2
D.-1, 1 + 2ω, 1 + 2ω2
Solution
(x - 1)3 + 8 = 0 ⇒ (x - 1) = (-2) (1)1/3
⇒ x - 1 = - 2 or - 2ω or -2ω2
or n = -1 or 1 - 2ω or 1 - 2ω2.
⇒ x - 1 = - 2 or - 2ω or -2ω2
or n = -1 or 1 - 2ω or 1 - 2ω2.
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