I will try.
the iy term is zero because the inputs are on the real axis.
f(x+iy) = x+a0-ib0/x+a0+ib0
Let x+a0+ib0 be d
Let x+a0-ib0 be conj(d)
then I end up with conj(d)/d
if there is an error in the logic I apologize. I am fairly new to this subject matter.
Homework Statement
Let a be a complex number for which Im(a) ≠ 0, and f(z) = (z + conj(a))/(z + a).
Prove f(z) maps the real axis onto the circle lwl = 1.
2. The attempt at a solution
I wrote out f(z) in an a+bi for and then with the Im(a) ≠ 0 I set the equation as
f(a+bi) =...
In the question below I do not understand what is meant by the "general form".
'Suppose f(z) = u(x,y) + i*v(x,y) is analytic on a domain D, and ux = 0 on D.
Find the general form of f(z).