QCE Specialist Mathematics – Complex Numbers, Trigonometry, Functions and Matrices Course Image 2

QCE Specialist Mathematics – Complex Numbers, Trigonometry, Functions and Matrices

2.1 Complex Numbres
2.2 Trigonometry
2.3 Graphs
2.4 Trigonometric Identities
2.5 Matrices

39 Lessons

In this course, students will develop the mathematical understanding and skills to solve problems relating to:

  • Complex Numbers 1
  • Trigonometry and Functions
  • Matrices

Complex numbers 1 introduces the complex plane, complex arithmetic and complex algebra. Trigonometry and functions build on the nature of proof and models periodic phenomena. Matrices introduce basic operations and extend to transformations in the plane.

These topics further develop the thinking techniques and mathematical rigour introduced in QCE Specialist Mathematics – Combinatorics, Vectors and Proof, and provide opportunities to nurture curiosity about the nature and utility of mathematics.

Source – QCAA General Senior Syllabus 2019


Complex Conjugates

Conjugates and Division of Complex Numbers

Properties of Conjugates

Square Roots of Complex Numbers

2-D Vectors


Complex Number Plane or Argand Diagram


Sine Equations in Radians

Cosine Equations in Radians

Tangent Equations in Radians

Quadratic Trigonometric Equations in Radians

General Solutions in Radians


Further Graphs of Absolute Value (Modulus) Functions

Logarithmic Graphs with Absolute Values

Reciprocal Functions

Graphs of Reciprocal Trigonometric Functions


Compound Angle Formula

Sums and Products of Sine and Cosine

Transformation Identities

Complementary Angle Formula

Trigonometric Models

Acceleration Given as a Rate of Change of Velocity

Simple Harmonic Motion: Velocity

Simple Harmonic Motion: Acceleration


Matrix Structure

Matrix Operations and Definitions

Matrix Algebra

Matrix Multiplication

Properties of Matrix Multiplication

Identity Matrix


Inverse of a Matrix

Matrix Equation

Transpose of a Matrix