Let a, b, x, y be real numbers such that a−b=1... | Complex Numbers | JEE Advance

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Question

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 $\operatorname{Im}\left(\frac{a z+b}{z+1}\right)=y$, then which of the following is(are) possible value(s) fo $x$ ?

Select ALL correct options:

A

$1-\sqrt{1+y^2}$

B

$-1-\sqrt{1-y^2}$

C

$1+\sqrt{1+y^2}$

D

$-1+\sqrt{1-y^2}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

⚠ Partially correct. Some answers are missing.

Solution

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Mathematics

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