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Consider the two complex numbers \( z \) and \( w \), such that \( w=\frac{z-1}{z+2}=a+i b \), where \( a, b \in R \) and \( i=\sqrt{-1} \).
\( \mathrm{P} \)
If \( z=C i S \theta \), which of the following does hold good?
W
(a) \( \sin \theta=\frac{9 b}{1-4 a} \)
(b) \( \cos \theta=\frac{1-5 a}{1+4 a} \)
(c) \( (1+5 a)^{2}+(3 b)^{2}=(1-4 a)^{2} \)
(d) All of these
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