In this Section:
In this section, we learn about the complex number system. At this point, we know that squaring a number in the real number system produces a non-negative result. This yields a problem when trying to take the square root of a negative number. Up to this point, we have simply stopped and reported the answer as “no real solution”. We introduce the imaginary unit “i” which is defined to be the square root of negative one. Using the imaginary unit i, we can perform operations in which we take the square root of a negative number. Additionally, we will learn about simplifying with the imaginary unit. We will learn how to rationalize a binomial denominator when the imaginary unit is involved. We will talk about how to perform operations with complex numbers and report the result in standard form: (a + bi). Lastly, we will learn how to simplify with powers of the imaginary unit i.