Perform computations involving complex numbers.
Some functions have zeros that are not real numbers. In order to find the zeros of such functions, we must consider the complex-number system.
We know that the square root of a negative number is not a real number. For example, is not a real number because there is no real number x such that . This means that certain equations, like or , do not have real-number solutions, and certain functions, like , do not have real-number zeros. Consider the graph of .
We see that the graph does not cross ...