Question 3 - A-Level Maths

Solve the equation \(z ^ { 2 } - 2 \mathrm { i } z - 5 = 0\), giving your answers in the form \(x + \mathrm { i } y\) where \(x\) and \(y\) are real.
Find the modulus and argument of each root.
Sketch an Argand diagram showing the points representing the roots.