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Let $ω \neq 1$ , be a cube root of unity, and $f : I \to C$ be defined by $f (n) = 1 + ω^{n} + ω^{2 n}$ then range of $f$ is

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Correct option is B

If n=3k,k∈I then f(n)=1+1+1=3If n=3k+1,k∈I then f(n)=1+ω+ω2=0If n = 3k + 2 k ∈ I, then f(n) = 1 + w2 + w = 0Thus, range of f is 0,3.

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Let ω≠1, be a cube root of unity, and f :I→C be defined by f(n)=1+ωn+ω2n then range of f is

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Let $ω \neq 1$ , be a cube root of unity, and $f : I \to C$ be defined by $f (n) = 1 + ω^{n} + ω^{2 n}$ then range of $f$ is