Complex Numbers #15

Algebra Level 3

If 1, a1, a2, a3 and a4 are the roots of x^5=1 and w is a complex cube root of unity, then the value of ((w-a1) (w-a2) (w-a3) (w-a4))/((w^2-a1) (w^2-a2) (w^2-a3) (w^2-a4))

w w^2 -1 1

1 solution

Aakhyat Singh
Mar 2, 2018

@Rishabh Cool , @Guillermo Templado , how did u solve this problem ?? Could u please post your solution to this problem ??

Of course, give me some time. I'll write it tonight or tomorrow morning, the value is $\frac{w^4 + w^3 + w^2 + w + 1}{w^8 + w^6 + w^4 + w^2 + 1} = \frac{w^4 + w^3}{w^8 + w^6} = \frac{w^3 \cdot (1 + w)}{w^6 \cdot (1 + w^2)} =$ $= \frac{- w^2}{ - w} = w$

Guillermo Templado - 3 years, 3 months ago

Complex Numbers #15

1 solution

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