Let \( a, b, x \) and \( y \) be real numbers such that \( a-b=1 \)...

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Let \( a, b, x \) and \( y \) be real numbers such that \( a-b=1 \) and \( y \neq 0 \). If the complex number \( z=x+ \) iy satisfies
\( \mathrm{P} \) \( \operatorname{Im}\left(\frac{a z+b}{z+1}\right)=y \), then which of the following is(are) possible value(s) of \( x \) ?
(A) \( -1+\sqrt{1-y^{2}} \)
(B) \( 1-\sqrt{1+y^{2}} \)
(C) \( 1+\sqrt{1+\mathrm{y}^{2}} \)
(D) \( -1-\sqrt{1-y^{2}} \)
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