(a)[5]
Without a calculator and with full working shown, determine the two square roots of $u$. Present your answers in the form $a + ib$, where the real numbers $a$ and $b$ are exact.
(b)[4]
On an Argand diagram, sketch the locus of points representing complex numbers $z$ that satisfy $|z - u| = 1$. Determine the largest value of $\arg z$ for points on this locus.