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Year 12 Maths
23. Imaginary and Complex Numbers
23.1 Introduction to imaginary numbers
Introduction to imaginary numbers
What You'll Learn
Define imaginary numbers using i, where i² equals negative one
Simplify square roots of negative numbers by extracting i
Perform arithmetic operations with imaginary numbers (addition, subtraction, multiplication, division)
Calculate powers of i by recognizing patterns in i², i³, i, and beyond
Convert expressions with negative radicals into imaginary number form
What You'll Practice
1
Simplifying roots of negative numbers like (-16) and (-40)
2
Evaluating powers of i from i³ to i²
3
Simplifying complex expressions with fractional exponents involving negative bases
4
Converting imaginary number expressions into simplified real or imaginary results
Why This Matters
Imaginary numbers are essential for solving equations that have no real solutions, like x² = -1. You'll use them throughout advanced algebra, precalculus, calculus, engineering, and physics to work with complex numbers, electrical circuits, and wave functions.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Practice exercises
Skills
Imaginary Numbers
Complex Numbers
Radicals
Exponents
Simplification
Powers of i
