The value of


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

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

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

Correct Option: , 2


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