Imaginary number facts for kids
Imaginary numbers are a special kind of number that helps us solve math problems we couldn't before. They are made using something called the imaginary unit, which is written as i. This i is very unique because when you multiply it by itself, you get -1. So, `i` multiplied by `i` equals -1 (`i^2 = -1`).
You might know that if you multiply a number by itself, like 3 x 3, you get 9. And if you multiply -3 x -3, you also get 9. There's no real number that you can multiply by itself to get a negative number. This is where imaginary numbers come in! They let us find the square root of negative numbers.
Imagine you are giving directions. If you say "go east by -1 mile", it's the same as saying "go west by 1 mile". Imaginary numbers work a bit like that, but for turning. If you say "go east by i miles", it means you turn to face north and go 1 mile. If you say "go east by -i miles", you turn to face south and go 1 mile.
Adding imaginary numbers is simple. If you say "go east by 1 + i miles", it means you go 1 mile east and then 1 mile north.
Multiplying imaginary numbers is like rotating. If you say "go east by 2 × -3 miles", it means you turn all the way around to face west, then go 6 miles. With imaginary numbers, you can turn part way. For example, "go east by 2 × 3i miles" means you turn to face north, then go 6 miles.
Contents
Why We Need Imaginary Numbers
For a long time, mathematicians couldn't solve problems like finding the square root of a negative number. For example, the square root of 9 is 3. But what about the square root of -9? We know that -3 multiplied by -3 is +9, not -9. So, there seemed to be no answer.
This is why mathematicians created the imaginary unit, i. They defined i as the main square root of -1. This new definition created a whole new type of number. Just like fractions gave us numbers like 2/3 that aren't whole numbers, and negative numbers gave us numbers less than zero, imaginary numbers gave us numbers that aren't on the regular number line. Even though they are called "imaginary," they are just as real and useful as any other number like 3 or 100.
Uses of Imaginary Numbers
Imaginary numbers are very important in many areas of science and engineering.
- Electrical engineering: Engineers use imaginary numbers (often called j to avoid confusion with electric current i) to understand how electric circuits work. This helps them design things like radios and computers.
- Physics: In fields like quantum physics and high energy physics, imaginary numbers are used all the time. Many important equations in the world cannot be solved without them.
Complex Numbers
Imaginary numbers can be mixed with the numbers we already know, called real numbers. For example, you can add a real number like 2 to an imaginary number like 3i. This creates a new number, 2 + 3i. These mixed numbers are called complex numbers.
Related pages
See also
In Spanish: Número imaginario para niños
