jee-advanced 2017 Q42

jee-advanced · India · paper1 Complex Numbers Arithmetic Systems of Equations via Real and Imaginary Part Matching

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 $\operatorname{Im}\left(\frac{az + b}{z + 1}\right) = y$, 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] $1 + \sqrt{1 + y^2}$
[D] $1 - \sqrt{1 + y^2}$

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 $\operatorname{Im}\left(\frac{az + b}{z + 1}\right) = y$, 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] $1 + \sqrt{1 + y^2}$

[D] $1 - \sqrt{1 + y^2}$

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