Answer 1

ω is a complex cube root of unity

∴ ω³ = 1 and 1 + ω + ω² = 0

Also, 1 + ω² = − ω, 1 + ω = − ω² and ω + ω² = − 1

L.H.S. = `("a" + "b"ω + "c"ω^2)/("c" + "a"ω + "b"ω^2)`

= `("a"ω^3 + "b"ω^4 + "c"ω^2)/("c" + "a"ω + "b"ω^2)`   ...[∵ ω³ = 1, ∴ ω⁴ = ω]

= `(ω^2("c" + "a"ω + "b"ω^2))/("c" + "a"ω + "b"ω^2)`

= ω²

= R.H.S.