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

Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

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)

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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

Watch 3-min video & get full concept clarity