Let z1,z2,z3 be three complex numbers such that z1+z2+z3=i,z1z2+z2z3+z1z3=−1,z1z2z3=−i. Let minimum value of |z1−kz2+(k−1)z3|∀ k∈[0,1] equals ‘a’ and minimum value of |z−z1|2+|z−z2|2+|z−z3|2∀ z∈C is ‘b’ (where i=−1, C is set of complex numbers)

zi=1,−1,i ; a = min. of |z1−kz2+(1−k)z3k+(1−k)|=1

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Let $z_{1}, z_{2}, z_{3}$ be three complex numbers such that $z_{1} + z_{2} + z_{3} = i, z_{1} z_{2} + z_{2} z_{3} + z_{1} z_{3} = - 1, z_{1} z_{2} z_{3} = - i .$ Let minimum value of $| z_{1} - k z_{2} + (k - 1) z_{3} | \forall k \in [0, 1]$ equals ‘a’ and minimum value of ${| z - z_{1} |}^{2} + {| z - z_{2} |}^{2} + {| z - z_{3} |}^{2} \forall z \in C$ is ‘b’ (where $i = \sqrt{- 1}$ , C is set of complex numbers)

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$z_{i} = 1, - 1, i$ ; a = min. of $| z_{1} - \frac{k z_{2} + (1 - k) z_{3}}{k + (1 - k)} | = 1$

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