Correct options (A) and (B)
It is given that z = x + iy satisfies Im(az + b/z + 1) = y
Therefore,
Rationalising the above equation: Multiplying and dividing LHS by (x + 1 - iy), we get
Using a2 - b2 = (a + b)(a - b), we get
Rearranging LHS, we get
ay - by/(x + 1)2 + y2 (as Im of the value in bracket is coefficient of i)
⇒ -y (a - b) = y(( x + y)2 ⇒(a - b) = (x + 1)2 + y2
It is given that a - b = 1 and y ≠ 0. Therefore,