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Sr please solve the problems
Asked by misra.dinesh2706 | 06 Jan, 2019, 08:43: AM
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, 03:19: PM
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