If - is a complex cube root of unity- then the value of a-b -c -2-c-a -b -2-a-b -c -2-b-c -b -2 is

A + b ω + c ω^2/c + a ω + b ω^2 = ω^2 and a + b ω + c ω^2/b + c ω + b ω^2 = ω ω^2 + ω = 1 ...

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Cube Root of a Complex Number

If ω is a com...

Question

If $ω$ is a complex cube root of unity, then the value of $\frac{a + b ω + c ω^{2}}{c + a ω + b ω^{2}}$ + $\frac{a + b ω + c ω^{2}}{b + c ω + b ω^{2}}$ is :

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1, ω, ω^{2}

\frac{(a + b ω + c ω^{2})}{(c + a ω + b ω^{2})} + \frac{(a + b ω + c ω^{2})}{(b + c ω + a ω^{2})}

ω

(1 - ω) (1 - ω^{2}) (1 - ω^{4}) (1 - ω^{8}) = α,

\frac{a + b ω + c ω^{2}}{b + c ω + a ω^{2}} + \frac{a + b ω + c ω^{2}}{c + a ω + b ω^{2}} = β

(\frac{a + b ω + c ω^{2}}{c + a ω + b ω^{2}}) + (\frac{a + b ω + c ω^{2}}{b + c ω + a ω^{2}})

\frac{a + b ω + c ω^{2}}{b + c ω + a ω^{2}} + \frac{a + b ω + c ω^{2}}{c + a ω + b ω^{2}}

p = a + b ω + c ω^{2}, q = b + c ω + a ω^{2}

r = c + a ω + b ω^{2}

a, b, c \neq 0

ω

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