Numbers Sequences and Series
Revision Guide
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
Full lenght Lecture Notes of the module available at
Recommended revision strategy
Make sure you are very comfortable with:
- The Definitions, Theorems, Proofs, and Examples contained in this Revision Guide
- The Tutorial and Homework questions
- The 2023/24 Exam Paper questions.
- The Checklist below
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