Complex Numbers 2 Question 18

18.

The points z1,z2,z3 and z4 in the complex plane are the vertices of a parallelogram taken in order, if and only if

(a) z1+z4=z2+z3

(b) z1+z3=z2+z4

(c) z1+z2=z3+z4

(d) None of these

(1983, 1M)

Show Answer

Answer:

Correct Answer: 18. (b)

Solution:

  1. Since, z1,z2,z3,z4 are the vertices of parallelogram.

∴ Mid-point of AC= mid-point of BD

⇒z1+z32=z2+z42⇒z1+z3=z2+z4

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