Complex Numbers And Quadratic Equations question 362
Question: If $ z=x+iy $ and $ |z-zi|=1, $ then [RPET 1988, 91]
Options:
A) $ z $ lies on $ x $ -axis
B) $ z $ lies on $ y $ -axis
C) z lies on a circle
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Here $ |z-zi|=1\Rightarrow |x+iy-i(x+iy)|=1 $
Þ $ |(x+y)+i(y-x)|=1 $
Þ $ 2x^{2}y^{2}=2x^{2}y^{2}+4x^{2} $
Þ $ 2(x^{2}+y^{2})=1 $ . Hence z lies on a circle.
BETA
