Complex Numbers And Quadratic Equations question 363
Question: The locus of $ z $ given by $ | \frac{z-1}{z-i} |=1 $ , is [Roorkee 1990]
Options:
A) A circle
B) An ellipse
C) A straight line
D) A parabola
Show Answer
Answer:
Correct Answer: C
Solution:
$ | \frac{z-1}{z-i} |=1 $
Þ $ |z-1|=|z-i| $
Þ $ |(x-1)+iy|=|x+i(y-1)| $
Þ $ \sqrt{{{(x-1)}^{2}}+y^{2}}=\sqrt{x^{2}+{{(y-1)}^{2}}} $
Þ $ 2x=2y $ or $ x-y=0 $ Which is the equation of a straight line.
BETA
