Question 5 - A-Level Maths

5 The complex number \(1 + \mathrm { i } \sqrt { 3 }\) is denoted by \(a\).

Find \(| a |\) and \(\arg a\).
Sketch on a single Argand diagram the loci given by \(| z - a | = | a |\) and \(\arg ( z - a ) = \frac { 1 } { 2 } \pi\).