If Re 1 2 z z i æ ö – ç ÷ è ø + = 1, where z = x + iy, then the point (x, y) lies on a:

Question:

If $\operatorname{Re}\left(\frac{z-1}{2 z+i}\right)=1$, where $z=x+i y$, then the point $(x, y)$ lies on $a$ :

  1. circle whose centre is at $\left(-\frac{1}{2},-\frac{3}{2}\right)$.

  2. straight line whose slope is $-\frac{2}{3}$.

  3. straight line whose slope is $\frac{3}{2}$.

  4. circle whose diameter is $\frac{\sqrt{5}}{2}$.

Correct Option: 4

JEE Main Previous Year 1 Question of JEE Main from Mathematics Complex Numbers and Quadratic Equations chapter.
JEE Main Previous Year Jan. 7, 2020 (I)

Solution:

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