Consider a complex number \( w=\frac{z-i}{2 z+1} \), where \( z=x+ \) iy and \( x, y \in R \). \...

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Consider a complex number \( w=\frac{z-i}{2 z+1} \), where \( z=x+ \) iy and \( x, y \in R \).
\( \mathrm{P} \)
If the complex number \( w \) is purely imaginary then locus of \( z \) is -
W
(A) a straight line
(B) a circle with centre \( \left(-\frac{1}{4}, \frac{1}{2}\right) \) and radius \( \frac{\sqrt{5}}{4} \).
(C) a circle with centre \( \left(\frac{1}{4},-\frac{1}{2}\right) \) and passing through origin.
(D) neither a circle nor a straight line.
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