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 \(z\) in the complex plane is
- A a circle
- B a parabola
- C a straight line
- D an ellipse
Answer & Solution
Correct Answer
(B) a parabola
Step-by-step Solution
Detailed explanation
Let \(z=x+i y\) \[ \begin{aligned} \therefore \frac{2 z+1}{i z+1} & =\frac{2(x+i y)+1}{i(x+i y)+1}=\frac{2 x+1+i y}{(-y+1)+i x} \\ & =\frac{[(2 x+1)+i y][(-y+1)-i x]}{[(-y+1)+i x][(-y+1)-i x]} \end{aligned} \]…
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