Question 8 - A-Level Maths

The complex number \(z\) is given by \(z = \frac { 4 - 3 \mathrm { i } } { 1 - 2 \mathrm { i } }\).
1. Express \(z\) in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.
2. Find the modulus and argument of \(z\).
Find the two square roots of the complex number 5-12i, giving your answers in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.