image of unit circle |z|=1 under the map f(z)=z+(1/z)

Answer 1

To find the image of the unit circle |z|=1 under the map f(z)=z+(1/z), we can substitute z=eiθ into f(z) and simplify:

f(eiθ) = eiθ + e-iθ
= 2cos(θ)

Therefore, the image of the unit circle |z|=1 under f(z) is the real axis, because all values of 2cos(θ) lie on the real line.