Question 1 - A-Level Maths

Exam Board	OCR MEI
Module	Further Pure Core (Further Pure Core)
Year	2023
Session	June
Topic	Complex Numbers Argand & Loci

The complex number \(\mathrm { a } + \mathrm { ib }\) is denoted by \(z\).
1. Write down \(z ^ { * }\).
2. Find \(\operatorname { Re } ( \mathrm { iz } )\).
The complex number \(w\) is given by \(w = \frac { 5 + \mathrm { i } \sqrt { 3 } } { 2 - \mathrm { i } \sqrt { 3 } }\).
1. In this question you must show detailed reasoning. Express \(w\) in the form \(\mathrm { x } + \mathrm { iy }\).
2. Convert \(w\) to modulus-argument form.