- A complex number \(z = x + \mathrm { i } y\) is represented by the point \(P\) in an Argand diagram.
Given that
$$| z - 3 | = 4 | z + 1 |$$
- show that the locus of \(P\) has equation
$$15 x ^ { 2 } + 15 y ^ { 2 } + 38 x + 7 = 0$$
- Hence find the maximum value of \(| z |\)