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

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Consider a complex number \( w=\frac{z-i}{2 z+1} \), where \( z=x+ \) iy and \( x, y \in R \).
PW
If the complex number \( w \) is purely real then locus of \( z \) is
(A) a straight line passing through origin
(B) a straight line with gradient 3 and \( y \) intercept \( (-1) \)
(C) a straight line with gradient 2 and y intercept 1 .
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