(i)[2]
Find the modulus and the argument of $u$.
(ii)[4]
Sketch an Argand diagram that displays the points for the complex numbers $1$, $i$ and $u$. Shade the set of points for the complex numbers $z$ that satisfy both inequalities $|z - 1| \leq |z - i|$ and $|z - u| \leq 1$.
(iii)[3]
Using your diagram, determine the value of $|z|$ for the point in this region whose $\arg z$ is least.