3.1 The Complex Numbers

  • 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.

The Complex-Number System

We know that the square root of a negative number is not a real number. For example, 1 is not a real number because there is no real number x such that x2=1. This means that certain equations, like x2=1 or x2+1=0, do not have real-number solutions, and certain functions, like f(x)=x2+1, do not have real-number zeros. Consider the graph of f(x)=x2+1.

We see that the graph does not cross ...

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