If z=a+ib, then the conjugate of z is a-ib. Therefore iz=ia-b. If iz=a-ib then a-ib=ia-b, so i(a+b)-(a+b)=(a+b)(i-1)=0. Since i doesn't equal 1, a=-b and z=a-ia and its conjugate is a+ia.
If x represents the real axis and y the imaginary axis z=a-ia means that x=a and y=-a so the line of reflection is y=-x. The complex number 2-i is the point where x=2 and y=-1, in other words, (2,-1). When reflected in y=-x, the x coordinate of 2 becomes y=-2 (because y=-x) and the y coordinate of -1 is reflected as x=1 (because x=-y), so the point (2,-1) is reflected as (1,-2). Converting this back to the complex number, we have 1-2i.