Complex Numbers And Quadratic Equations question 359
Question: If the imaginary part of $ \frac{2z+1}{iz+1} $ is -2, then the locus of the point representing $ z $ in the complex plane is [DCE 2001]
Options:
A) A circle
B) A straight line
C) A parabola
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ \frac{2z+1}{iz+1}=\frac{2(x+iy)+1}{i(x+iy)+1}=\frac{(2x+1)+2iy}{(1-y)+ix} $ $ =\frac{[(2x+1)(1-y)+2xy]+i[2y(1-y)-x(2x+1)]}{{{(1-y)}^{2}}+x^{2}} $ But it is given that imaginary part of $ \frac{(2z+1)}{(iz+1)} $ is - 2 Þ $ x+2y-2=0 $ . Which is a straight line.
BETA
