A linear mapping is a function defined by f (z) = az + b, where a = 0 and a and b are constants that may be complex. Here are special cases:

1. If f (z) = z+ b, then f is a translation. 2. If f (z) = αz and α is real, then f is amagnification (or compression or dilation). In

the future we may refer to a mapping as a magnification even if |α| < 1. 3. If f (z) = eiϕz, where ϕ is real, then f is a rotation, because f (reiθ ) = rei(θ+ϕ).