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Sr please solve the problems 
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Asked by misra.dinesh2706 | 06 Jan, 2019, 08:43: AM
answered-by-expert Expert Answer
In order to maximize |Z1-Z2|  let us assume these complex numbers are on x-axis and symmetrically placed with respect to origin.
 
Z1 = 1  and Z2 = -1
 
Let Z3  = cosθ+ i sinθ
 
|Z1 - Z2|2  = 4
 
Z1 - Z3 = (1- cosθ ) - i sinθ  and  Z2 - Z3 = -(1+cosθ) - i sinθ
 
|Z1-Z3|2 = (1-cosθ)2 + sin2θ = 2 - 2cosθ
 
|Z2-Z3|2 = (1+cosθ)2 + sin2θ = 2 + 2cosθ
 
hence maximum value of |Z1 - Z2|2 + |Z2-Z3|2 + |Z3-Z1|2 = 4+2 + 2cosθ+2 - 2cosθ.
Now you can calculate the final answer.
Answered by | 07 Jan, 2019, 15:19: PM

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