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If z1, z2 and z3 are three complex numbers such that |z1|=2, |z2|=3 and |z3|=4, then what is the maximum value of |z1-z2|^2+|z2-z3|^2+|z3-z1|^2 ?

If z1, z2 and z3 are three complex numbers such that |z1|=2, |z2|=3 and |z3|=4, then what is the maximum value of |z1-z2|^2+|z2-z3|^2+|z3-z1|^2 ?

Grade:12th pass

1 Answers

Vikas TU
14149 Points
5 years ago
 = k letk = (|z1| + |z2|)^2 + (|z2| + |z3|)^2 + (|z3| + |z1|)^2)maximum value of |z1-z2|^2+|z2-z3|^2+|z3-z1|^2 
  = ( 2 + 3)^2 + (3 + 4)^2 + (4 + 2)^2
 = 25 + 49 + 36
= 110.
By using simple maxima and minima properties of z- complex no. U can solve this simply.
 
Hope it helps!

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