Section 1
Definition of Imaginary Unit i
Property
Imaginary Unit:
or
In this Grade 4 AMC Math lesson from AoPS: Introduction to Algebra, students explore imaginary numbers by learning how the unit imaginary number i is defined through the equation i² = -1. Students practice evaluating expressions like (3i)² and (ai)², solve equations such as x² = -16 by expressing solutions in the form ±bi, and discover the repeating four-cycle pattern of powers of i. The lesson builds foundational understanding of imaginary numbers as distinct from real numbers on the number line.
Section 1
Definition of Imaginary Unit i
Imaginary Unit:
or
Section 2
Square Root of Negative Numbers
The imaginary unit is the number whose square is .
Square Root of a Negative Number
Section 3
Squaring Imaginary Numbers
To square an imaginary number of the form , use:
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Section 1
Definition of Imaginary Unit i
Imaginary Unit:
or
Section 2
Square Root of Negative Numbers
The imaginary unit is the number whose square is .
Square Root of a Negative Number
Section 3
Squaring Imaginary Numbers
To square an imaginary number of the form , use:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter