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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.
x = 2 or -2
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