Question

if X+iy^a=alfa^alfa+ beta​

Answer 1

Answer:

Given x = a+b, y = aα +bβ and z = aβ+bα

α,β are cube roots of unity.

So α = ω, β = ω2

xyz = (a+b)(aα +bβ)( aβ+bα)

= (a+b)(a2αβ+abα2+abβ2+b2αβ)

= (a+b)(a2αβ+ab(α2+β2)+b2αβ)

Substitute α and β in above equation

= (a+b)(a2(ωω2)+ab(ω2+ω4)+b2(ωω2))

= (a+b)(a2-ab+b2)

= a3+b3

Hence option (3) is the answer.