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If $z_{1}, z_{2}, z_{3}$ be three complex number such than $z_{1} + z_{2} + z_{3} = 0$ and $|z_{1}| = |z_{2}| = |z_{3}| = 1$ than $|z_{1}^{2} + 2 z_{2}^{2} + z_{3}^{2}|$ equals

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Correct option is A

z1+z2+z3=0⇒z¯1+z¯2+z¯3=0⇒1z1+1z2+1z3=0 ∵z1z¯1=1 etc. Now, 0=z1+z2+z32=z12+z22+z32+2z2z3+z3z1+z1z2⇒0=z12+z22+z32+2z1z2z31z1+1z2+1z3=z12+z22+z32Thus, z12+2z22+z32=z12+z22+z32+z22=0+z22=z22=1

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If z1,z2,z3 be three complex number such than z1+z2+z3=0 and z1=z2=z3=1 than z12+2z22+z32 equals

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If $z_{1}, z_{2}, z_{3}$ be three complex number such than $z_{1} + z_{2} + z_{3} = 0$ and $|z_{1}| = |z_{2}| = |z_{3}| = 1$ than $|z_{1}^{2} + 2 z_{2}^{2} + z_{3}^{2}|$ equals