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Properties of Determinants

If ω is a com...

Question

If ω is a complex cube root of unity, then the value of the

A

0

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B

ω

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C

2

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D

4

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Solution

The correct option is D
4

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ω

is complex cube root of unity , then

(1 - ω + ω^{2})^{6} + (1 - ω^{2} + ω)^{6} =

ω

is a complex cube root of unity, then the value of

(1 + ω) (1 + ω^{2}) (1 + ω^{4}) (1 + ω^{8}) . . . (2 n + 1)

ω

is a complex cube root of unity, then a root of the equation

∣ ∣ ∣ ∣ ∣ \begin{matrix} x + 1 & ω & ω^{2} ω & x + ω^{2} & 1 ω^{2} & 1 & x + ω \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

^{'} ω^{'}

is a complex cube root of unity, then

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

ω

is the complex cube root of unity, then the value of

ω + ω^{(\frac{1}{2} + \frac{3}{8} + \frac{9}{32} + \frac{27}{128} + . . . .)}

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