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If $z_{1} + z_{2} + z_{3} = 0$ and $|z_{1}| = |z_{2}| = |z_{3}| = 1,$ then value of $z_{1}^{2} + z_{2}^{2} + z_{3}^{2}$ equals

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Correct option is B

z12+z22+z32=z1+z2+z32−2z2z3+z3z1+z1z2=0−2z1z2z31z1+1z2+1z3=−2z1z2z3z¯1+z¯2+z¯3=−2z1z2z3(0)=0 ∵z1=z2=z3=1

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If z1+z2+z3=0 and z1=z2=z3=1, then value of z12+z22+z32 equals

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Ready to Test Your Skills?

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If $z_{1} + z_{2} + z_{3} = 0$ and $|z_{1}| = |z_{2}| = |z_{3}| = 1,$ then value of $z_{1}^{2} + z_{2}^{2} + z_{3}^{2}$ equals