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Topic 1: Complex numbers

Introduction to complex numbers

4 hours

• Define the imaginary number i as a root (solution) of the equation x² = −1. 1 interactive
• Define and use set notation of the number system for complex numbers (ℂ).
• Use complex numbers in the form a + bi where a and b are the real and imaginary parts (components) Re(z) and Im(z) of a complex number z.
• Determine and use complex conjugates.
• Perform complex-number arithmetic — addition, subtraction, multiplication and division — with and without technology.

The complex plane (the Argand plane)

6 hours

• Sketch and use complex numbers as points in the complex plane with real and imaginary parts as Cartesian coordinates.
• Understand and use addition of complex numbers as vector addition in the complex plane. 1 interactive
• Understand and use location of complex conjugates in the complex plane. 1 interactive
• Understand and use multiplication by a complex number as a linear transformation in the complex plane. 1 interactive