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JEE Main · 2011 · 10 Apr 2011 · Offline · Complex Numbers

If

ω (\neq = 1)

is a cube root of unity, and

(1 + ω)^{7} = A + B ω

. Then

(A, B)

equals

(A)(1,1)✓ Correct
(B)(1,0)
(C)(-1,1)
(D)(0,1)

Answer: (A)

Solution

Since

1 + ω + ω^{2} = 0

for a non-real cube root of unity,

1 + ω = - ω^{2}

. Then

(1 + ω)^{7} = (- ω^{2})^{7} = - ω^{14}

, and because

ω^{3} = 1

,

ω^{14} = ω^{2}

, so

(1 + ω)^{7} = - ω^{2} = 1 + ω

. Matching with

A + B ω

gives

A = 1

and

B = 1

, so

(A, B) = (1, 1)

.

JEE Main · 2011 · 10 Apr 2011 · Offline · Single correct option

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