Question 8 - A-Level Maths

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2004
Session	June
Topic	Complex Numbers Arithmetic
Type	Standard quadratic with real coefficients

Find the roots of the equation \(z ^ { 2 } - z + 1 = 0\), giving your answers in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.
Obtain the modulus and argument of each root.
Show that each root also satisfies the equation \(z ^ { 3 } = - 1\).