it is given that a +ib = c+i / c-i .
mod or taking magnitudes on both sides : root a+ib2 = [root c+i / rootc-1] 2 ==> root a2 + b2 = 1
squaring on both sides , a2 + b2 = 1
to bring the complex number in std form , we can multiply both nr and dr by c+i
==> (c+i)2 / c2 + 1 ==> c2+2ci -1 / c2 +1 ==> a = c2 - 1/ c2+1 , b = 2c / c2 +1
==> b / a = 2c / c2-1 ( c2+1 get cancelled )
hope u got it