Complex Numbers And Quadratic Equations question 70
Question: The values of $ z $ for which $ |z+i|=|z-i| $ are [Bihar CEE 1994]
Options:
A) Any real number
B) Any complex number
C) Any natural number
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ z=x+iy $ ……(i) Given $ |z+i|=|z-i| $ or $ |x+iy+i|=|x+iy-i| $ or $ |x+i(y+1)|=|x+i(y-1)| $ or $ \sqrt{x^{2}+{{(y+1)}^{2}}}=\sqrt{x^{2}+{{(y-1)}^{2}}} $ or $ x^{2}+{{(y+1)}^{2}}=x^{2}+{{(y-1)}^{2}} $ or $ y^{2}+2y+1=y^{2}-2y+1 $ or $ 4y=0 $ or $ y=0 $ Hence from (i), we get $ z=x $ , where $ x $ is any real number.
BETA
