We learned before t hat the square root of a number is never negative. It is always positive. Nevertheless, mathematicians have invented such a number. So for the purpose of mathematicians, they do exist. These are called complex numbers. The square root of -1 is particular important for us. It is denoted i. When we see i^2, we must keep in mind that the answer is -1. Nevertheless, i can be used generically to represent the square root of any negative number. We use i to represent the square root of -b, which is the square root of any negative number.
The function of i is to help us to determine the square root of negative real numbers. Keeping in mind that i represents the square root of negative 1, we can use it to help determine the square root of negative numbers by writing -b under a square root sign, which represents the square root of a negative real number, and then write that this is equal to bi. As an example, we can write -4 under a square root sign, representing the square eroot of negative three, and then we can write that this is equal to 4i, which is equal to 2. Thus, keep in mind what we have said before about how a square has both a negative and positive square root. This is the case because we can obtain 4 by multiplying either 2 by itself or also -2 by itself.
We represent complex numbers with the expression a + bi, where a and b are real numbers. These can be either integers or fractions. Where a is a 0, as in the example of 0 + 5i, we can simply write 5i. When we lack the i, this means the expression of the complex number is 0. Thus, if we were to simply write 5, this would be the equivalent of 5 + 0i.