On a single Argand diagram sketch the loci given by the equations \(| z - 3 + 2 i | = 2\) and \(| w - 3 + 2 \mathrm { i } | = | w + 3 - 4 \mathrm { i } |\) where z and \(w\) are complex numbers.
Hence find the least value of \(| \mathbf { z } - \mathbf { w } |\) for points on these loci. Give your answer in an exact form.