What is an Imaginary Number?
The square root of a negative number, usually expressed using i
An imaginary number is a number that involves the square root of a negative number, which is something we can’t do using only real numbers. In math, we use the symbol i for the square root of a negative number and say i² = –1, so that i = √(–1).
So:
- i² = –1
- √(–1) = i and
- 2i means 2 × √(–1)
Even though they’re called "imaginary," these numbers are used in real mathematical situations and advanced topics like engineering, physics, and electronics.
Imaginary numbers combine with real numbers to form complex numbers, like:
- 3 + 2i
- –1 – 5i
These help solve problems that regular numbers (real numbers) can’t.
When Do Students Learn About Imaginary Numbers?
Students begin learning about imaginary numbers in high school when they work with square roots of negative numbers and complex numbers.
Grades 9+ – Introduction to Imaginary and Complex Numbers
Students explore imaginary numbers as they expand their understanding of square roots, quadratic equations, and complex number systems.
