Question 2 - A-Level Maths

Exam Board	OCR MEI
Module	Further Pure Core (Further Pure Core)
Year	2024
Session	June
Topic	Complex Numbers Arithmetic
Type	Multi-part questions with division as one step

2 Two complex numbers are given by \(u = - 1 + \mathrm { i }\) and \(v = - 2 - \mathrm { i }\).

1. Find \(\mathrm { u } - \mathrm { v }\) in the form \(\mathrm { a } + \mathrm { bi }\), where \(a\) and \(b\) are real.
2. In this question you must show detailed reasoning. Find \(\frac { \mathrm { u } } { \mathrm { v } }\) in the form \(\mathrm { a } + \mathrm { bi }\), where \(a\) and \(b\) are real.
Express \(u\) in exact modulus-argument form.