Complex Numbers And Quadratic Equations question 377
Question: If $ w=\frac{z}{z-\frac{1}{3}i} $ and $ |w|=1 $ , then z lies on [AIEEE 2005]
Options:
A) A straight line
B) A parabola
C) An ellipse
D) A circle
Show Answer
Answer:
Correct Answer: A
Solution:
$ | \frac{z}{z-\frac{i}{3}} |=1\Rightarrow |z|=| z-\frac{i}{3} | $ Clearly locus of z is perpendicular bisector of line joining points having complex number $ 0+i0 $ and $ 0+\frac{i}{3} $ . Hence z lies on a straight line.
BETA
