Complex Numbers 2 Question 18

18.

The points $z _1, z _2, z _3$ and $z _4$ in the complex plane are the vertices of a parallelogram taken in order, if and only if

(a) $z _1+z _4=z _2+z _3$

(b) $z _1+z _3=z _2+z _4$

(c) $z _1+z _2=z _3+z _4$

(d) None of these

(1983, 1M)

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Answer:

Correct Answer: 18. (b)

Solution:

  1. Since, $z _1, z _2, z _3, z _4$ are the vertices of parallelogram.

$\therefore$ Mid-point of $A C=$ mid-point of $B D$

$ \begin{array}{ll} \Rightarrow & \frac{z _1+z _3}{2}=\frac{z _2+z _4}{2} \\ \Rightarrow & z _1+z _3=z _2+z _4 \end{array} $



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