If - is complex cube root of unity then value of 2-5-2-26-2-2-5-26 is

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Cube Root of a Complex Number

If ω is com...

Question

If $ω$ is complex cube root of unity then value of $(2 + 5 ω + 2 ω^{2})^{6} - (2 + 2 ω + 5 ω^{2})^{6} i s$

3^{6}

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3^{7}

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0

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243

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Solution

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ω

(2 + 5 ω + 2 ω^{2})^{6} = (2 + 2 ω + 5 ω^{2})^{6} = 729

ω \neq 1

(1 + 2 ω + 2 ω^{2})^{10} + (2 + ω + 2 ω^{2})^{10} + (2 + 2 ω + ω^{2})^{10}

ω

2 ω

2 ω^{2}

\frac{1}{1 + 2 ω} + \frac{1}{2 + ω} - \frac{1}{1 + ω} = 0

ω

\frac{1}{1 + 2 ω} + \frac{1}{2 + ω} - \frac{1}{1 + ω} = 0

ω

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