Numbers Sequences and Series

Revision Guide

Author
Affiliation

University of Hull

Published

21 Nov 2024

Revision Guide

Revision Guide document for the module Numbers Sequences and Series 400297 2024/25 at the University of Hull. If you have any question or find any typo, please email me at

S.Fanzon@hull.ac.uk

Full lenght Lecture Notes of the module available at

silviofanzon.com/2024-NSS-Notes

Checklist

You should be comfortable with the following topics/taks:

Preliminaries

  • Prove that \(\sqrt{p} \notin \mathbb{Q}\) for \(p\) a prime number

Complex Numbers

  • Sum, multiplication and division of complex numbers
  • Computing the complex conjugate
  • Computing the inverse of a complex number
  • Find modulus and argument of a complex number
  • Compute Cartesian, Trigonometric and Exponential form of a complex number
  • Complex exponential and its properties
  • Computing powers of complex numbers
  • Solving degree 2 polynomial equations in \(\mathbb{C}\)
  • Long division of polynomials
  • Solving higher degree polynomial equations in \(\mathbb{C}\)
  • Finding the roots of unity
  • Finding the n-th roots of a complex number