Let α & β are roots of x2+ωx+ω2=0, where ω is an imaginary cube root of unity and z=α9+iβ9, then value of |z| is

Given equation is x2+ωx+ω2=0⇒x2−1+ω2x+ω2=0 ∴1+ω+ω2=0⇒ω=−1+ω2⇒α=1,β=ω2 are roots of the equation ∴z=α9+iβ9=(1)9+iω29=1+i Hence, |z|=1+1=2