Find the two square roots of the complex number \(- 3 + 4 \mathrm { i }\), giving your answers in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.
The complex number \(z\) is given by
$$z = \frac { - 1 + 3 \mathrm { i } } { 2 + \mathrm { i } } .$$
Express \(z\) in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.
Show on a sketch of an Argand diagram, with origin \(O\), the points \(A , B\) and \(C\) representing the complex numbers \(- 1 + 3 \mathrm { i } , 2 + \mathrm { i }\) and \(z\) respectively.
State an equation relating the lengths \(O A , O B\) and \(O C\).