Hi everyone, this is my first time on this forum, so please bear with me.

I am currently going over some paper and came across this:

Let x, y be complex #s and IxI+IyI=1. If a,b are also elements of complex numbers and Ix +/- aI + Iy +/- bI <= 1

The author claims that if x*y is not 0, then

I IxI +/- a*(IxI/x)I + I IyI +/- b*(IyI/y)I <=1

Sorry about this notation, IxI denotes the modulus of x and +/- means + or -. Any help is appreciated. Thanks!