Complex Numbers And Quadratic Equations question 353
Question: The complex numbers $ z=x+iy $ which satisfy the equation $ | \frac{z-5i}{z+5i} |=1 $ lie on [IIT 1982]
Options:
A) Real axis
B) The line $ y=5 $
C) A circle passing through the origin
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ | \frac{z-5i}{z+5i} |=1 $
Þ $ | \frac{x+i(y-5)}{x+i(y+5)} |=1 $
Þ $ |x+i(y-5)|=|x+i(y+5)| $ , $ ( \because | \frac{z_1}{z_2} |=\frac{|z_1|}{|z_2|} ) $
Þ $ x^{2}+25-10y+y^{2}=y^{2}+x^{2}+25+10y $
Þ $ 20y=0 $
Þ $ y=0 $ .
BETA
