( z + a ) ( ¯¯¯z+a) , where a is real , is equivalent to :
z¯¯¯z=|z|2
So ( z +a ) ( ¯¯¯z+a) = (z +a ) ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(z+a)=|z+a|2