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:
- 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} $
