Complex Numbers 2 Question 21

22.

The complex numbers z=x+iy which satisfy the equation z−5iz+5i=1, lie on

(1981, 2M)

(a) the X-axis

(b) the straight line y=5

(c) a circle passing through the origin

(d) None of the above

Show Answer

Answer:

Correct Answer: 22. (a)

Solution:

  1. Given, |z−5iz+5i|=1⇒|z−5i|=|z+5i|

[∵ if |z−z1|=|z−z2|, then it is a perpendicular bisector of z1 and z2]

∴ Perpendicular bisector of (0,5) and (0,−5) is X-axis.

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