Showing all your working and without the use of a calculator, find the square roots of the complex number \(7 - ( 6 \sqrt { } 2 ) \mathrm { i }\). Give your answers in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real and exact.
On an Argand diagram, sketch the loci of points representing complex numbers \(w\) and \(z\) such that \(| w - 1 - 2 \mathrm { i } | = 1\) and \(\arg ( z - 1 ) = \frac { 3 } { 4 } \pi\).
Calculate the least value of \(| w - z |\) for points on these loci.