Complex Numbers And Quadratic Equations question 381
Question: The number of solutions for the equations $ |z-1|=|z-2|= $ $ |z-i| $ is [Orissa JEE 2005]
Options:
A) One solution
B) 3 solutions
C) 2 solutions
D) No solution
Show Answer
Answer:
Correct Answer: A
Solution:
From $ |z-1|=|z-2| $
Þ $ |x+iy-1|=|x+iy-2| $
Þ $ {{(x-1)}^{2}}+y^{2}={{(x-2)}^{2}}+y^{2} $
Þ $ x=\frac{3}{2} $ Similarly from $ |z-1|=|z-i| $ ; $ x=y $ Hence, $ x=\frac{3}{2},y=\frac{3}{2} $ Therefore only one solution for the equation.
BETA
