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If $z^{2} + z + 1 = 0,$ where $z$ is a complex number, then values of $S = {(z + \frac{1}{z})}^{2} + {(z^{2} + \frac{1}{z^{2}})}^{2} + {(z^{3} + \frac{1}{z^{3}})}^{2} + \dots + {(z^{6} + \frac{1}{z^{6}})}^{2}$ is

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Correct option is A

z2+z+1=0 ⇒ z=ω,ω2.Let z=ω then (ω+ω2)2 =ω2+ω42=ω4+ω82=ω5+ω102=1and ω3+ω62=ω6+ω122=4.Thus, S=12.

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If z2+z+1=0, where z is a complex number, then values of S=z+1z2+z2+1z22+z3+1z32+⋯+z6+1z62 is

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If $z^{2} + z + 1 = 0,$ where $z$ is a complex number, then values of $S = {(z + \frac{1}{z})}^{2} + {(z^{2} + \frac{1}{z^{2}})}^{2} + {(z^{3} + \frac{1}{z^{3}})}^{2} + \dots + {(z^{6} + \frac{1}{z^{6}})}^{2}$ is