Let z1,z2 and z3 be three complex numbers such that |z1|=|z2|=|z3|=1 a – InterviewSolution

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1.	Let z1,z2 and z3 be three complex numbers such that \|z1\|=\|z2\|=\|z3\|=1 and z21z2z3+z22z3z1+z23z1z2+1=0. Then the sum of all possible values of \|z1+z2+z3\| is
Answer» Let $z_{1}, z_{2}$ and $z_{3}$ be three complex numbers such that $\| z_{1} \| = \| z_{2} \| = \| z_{3} \| = 1$ and $\frac{z_{1}^{2}}{z_{2} z_{3}} + \frac{z_{2}^{2}}{z_{3} z_{1}} + \frac{z_{3}^{2}}{z_{1} z_{2}} + 1 = 0.$ Then the sum of all possible values of $\| z_{1} + z_{2} + z_{3} \|$ is

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