Which of the following statements is FALSE?f(z)=z + 1/z+1 is a fractional linear transformationf(z) = z is a conformal map from the right half-plane {z

Which of the following statements is FALSE?f(z)=z + 1/z+1 is a fractional linear transformationf(z) = z² is a conformal map from the right half-plane {z : Re(z)>0} onto its imageIf f is a fractional linear transformation with f(x) = ?, then f must be affineThe image of a circle in the plane under a conformal map is not necessarily a circle