Year 9
Mathematics
Number & Algebra
AC9M9N02
Introduction to Complex Numbers
Complex numbers extend the real number system by introducing i, the square root of -1. They have a real part and an imaginary part.
What You Need to Know
Key Concept Diagram
i is defined as the square root of -1, so i^2 = -1
A complex number has the form a + bi where a is real and b is imaginary
To add complex numbers, add real parts and imaginary parts separately
The conjugate of a + bi is a - bi; multiplying them gives a^2 + b^2
Key Vocabulary
Imaginary unit
i, defined as the square root of -1
Complex number
A number of the form a + bi with real and imaginary parts
Real part
The a in a + bi
Conjugate
The complex number with the sign of the imaginary part reversed
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is i^2?
Question 2
Add (3 + 2i) + (1 - 5i).
Question 3
The conjugate of 4 - 3i is:
Key Concepts Summary
- ●i is defined as the square root of -1, so i^2 = -1
- ●A complex number has the form a + bi where a is real and b is imaginary
- ●To add complex numbers, add real parts and imaginary parts separately
- ●The conjugate of a + bi is a - bi; multiplying them gives a^2 + b^2