TS EAMCET · Maths · Complex Number
If the imaginary part of \(\frac{2 z+1}{i z+1}\) is -2 , then the locus of the point representing \(\mathrm{z}\) in the Argand plane is
- A a circle
- B a straight line
- C a parabola
- D an ellipse
Answer & Solution
Correct Answer
(B) a straight line
Step-by-step Solution
Detailed explanation
\begin{aligned} & \frac{2 z+1}{i z+1}=\frac{(2 x+1)+2 y i}{(1-y)+x i} \\ = & \frac{(2 x+1)+2 y i}{(1-y)+x i} \times \frac{(1-y)-x i}{(1-y)-x i} \\ \because & \text { Imaginary part }=-2 \\ \therefore \quad & \frac{-x(2 x+1)+2 y(1-y)}{(1-y)^2+x^2}=-2 \\ \Rightarrow & -2 x^2-x+2…
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