# Topic 1 – Core: Algebra

## Sequences and Series

## Working with Sequences and Series

## Arithmetic Progressions

## Geometric Series

## Logarithmic and Exponential Functions

## Exponential Functions and Logarithms

## The Exponential Function e^{x} and Natural Log Functions

## Permutations and Combinations

## Sequences and Series

## Proof by mathematical induction

## Sum of Series

## Various Types of Proofs

## Complex Numbers

## Complex Numbers

- Real and imaginary numbers
- Addition, subtraction and multiplying complex numbers and simplifying powers of i
- Division of a complex number by a complex number
- Argand diagrams
- Modulus and argument of a complex number
- Solving problems with complex numbers
- Square roots of a complex number
- Solving quadratic equations with complex roots
- Solving cubic equations
- Solving quartic equations
- Exam Questions - Complex numbers
- Exam Questions - Finding roots
- Modulus-argument form of a complex number
- Exponential Form (Euler's relation)
- Multiplication and division rules for mod and argument of two complex numbers
- Exam Questions - Further complex numbers
- Complex numbers specimen questions (mixed exam boards)