(a)[5]
Without using a calculator and showing all your working, determine the square roots of the complex number $7 - 6\sqrt{2}i$. Present your answers in the form $x + iy$, where $x$ and $y$ are real and exact.
(b(i))[4]
On an Argand diagram, draw the loci corresponding to complex numbers $w$ and $z$ that satisfy $|w - 1 - 2i| = 1$ and $\arg(z - 1) = \frac{3}{4}\pi$.
(b(ii))[2]
Calculate the least value of $|w - z|$ for points on these loci.