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Question
If ω(≠1) is a cube root of unity and (1 + ω)7 = A + Bω, then A and B are respectively the numbers ______.
Options
0, 1
1, 1
1, 0
−1, 1
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Solution
If ω(≠1) is a cube root of unity and (1 + ω)7 = A + Bω, then A and B are respectively the numbers 1, 1.
Explanation:
ω is a cube root of unity
⇒ 1 + ω + ω2 = 0
⇒ 1 + ω = – ω2
⇒ (1 + ω)7 = (– ω2)7
= – ω14
= – ω12 × ω2
= – ω2
= 1 + ω
= A + ω.B
A = 1, B = 1
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