Why is i one of the solutions to the equation x2 equals -1?

Answer 1

3

Answer 2

x2 = -1

Therefore x must equal the square root of -1. However, there is no number that is the square root of a negative number!

The square root of a number is a number that when multiplied by itself will result in the original number.

So the square root of 4 is 2, as 2 * 2 = 4.

However, there is no number that when multiplied by itself can result in a negative number. This is because 2 negative numbers multiplied together (or 2 positive numbers) alwaysresult in a positive number.

So we can say that there is no real number that is equal to the square root of -1. Mathematicians decided to invent what are known as imaginary numbers! They decided that the square root of -1 would be known as i.

This meant that the square roots of all negative numbers could now be expressed in terms of the square root of a positive number multiplied by i.

Let us look at a quick example to show this:

The square root of 36 is 6 of course.

36 is of course also equal to 9 * 4. We can therefore also say that the square root of 36 must be equal to the square root of 9 multiplied by the square root of 4 (i.e. 3 * 2 = 6)

Similarly, using exactly the same principles, we can write that the square root of, for example, -36 is equal to the square root of 36 multiplied by the square root of -1. We have agreed that the square root of -1 is i. Thus it must equal 6 * i = 6i.