Question 3 - A-Level Maths

Exam Board	Edexcel
Module	FP1 (Further Pure Mathematics 1)
Topic	Complex Numbers Arithmetic
Type	Multi-part questions with division as one step

3. \(z = 1 + \mathrm { i } \sqrt { 3 }\) Express in the form \(a + \mathrm { i } b\), where \(a\) and \(b\) are real.

\(z ^ { 2 } + z\),
\(\frac { z } { 3 - z }\),
giving the exact values of \(a\) and \(b\) in each part.