6 In an Argand diagram, the variable point \(P\) represents the complex number \(z = x + \mathrm { i } y\), and the fixed point \(A\) represents \(a = 4 - 3 \mathrm { i }\).
- Sketch an Argand diagram showing the position of \(A\), and find \(| a |\) and \(\arg a\).
- Given that \(| z - a | = | a |\), sketch the locus of \(P\) on your Argand diagram.
- Hence write down the non-zero value of \(z\) corresponding to a point on the locus for which
(a) the real part of \(z\) is zero,
(b) \(\quad \arg z = \arg a\).