−1 (number) facts for kids

In mathematics, −1 is a special integer. It is the number you add to 1 to get 0. Think of it as the "opposite" of 1. If you have 1 apple and someone takes 1 apple away, you have 0 apples left.

Negative one is a negative number. It sits on the number line between negative two (−2) and zero (0). It has some things in common with positive one, but also some big differences!

In computer science, −1 is often used as a starting number for counting. It can also show that a computer program hasn't found any useful information yet. It's like a placeholder.

What Happens When You Multiply by -1?

Multiplying any number by −1 simply changes its sign. For example, if you multiply 5 by −1, you get −5. If you multiply −5 by −1, you get 5.

This happens because −1 is the "additive inverse" of 1. This means that when you add 1 and −1 together, you get 0.

Squaring -1: What's the Result?

When you square a number, you multiply it by itself. So, squaring −1 means you multiply −1 by −1. The amazing thing is that −1 multiplied by −1 equals 1!

This is why the square of any negative number is always a positive number. For example, −2 times −2 equals 4.

The Square Roots of -1

Normally, when you take the square root of a number, you're looking for a number that, when multiplied by itself, gives you the original number. For example, the square root of 4 is 2 (because 2 times 2 is 4).

But what about the square root of −1? There is no "normal" number that you can multiply by itself to get −1. This is where complex numbers come in!

Mathematicians created a special number called i (the imaginary unit). By definition, i multiplied by i (or i²) equals −1. So, i is a square root of −1. The only other complex number that works is −i.

This picture shows 0, 1, −1, i, and −i on a special graph called the complex plane.

Using Negative Numbers as Powers

You can also use negative numbers as powers (or exponents). When a number has a power of −1, it means you take its reciprocal.

For example, x⁻¹ is the same as 1 divided by x (written as 1/x). So, 5⁻¹ is 1/5. This rule works for any number that isn't zero.

How Computers Store -1

Computers need a way to store negative numbers like −1. The most common way they do this is using something called "two's complement". This is a clever system that lets computers represent both positive and negative numbers using only ones and zeros.

See also

In Spanish: Menos uno para niños