Though some believe that the idea of imaginary numbers may have been discovered some 4,000 years ago, society did not see its necessity until the 16th century. Until that time, history has recorded several instances where people have stumbled upon the idea of imaginary numbers but made little advancements on the idea because most people saw them as being impossible. The link above will display a list that explains some of the notable discoveries that directly impacted the development of imaginary numbers (Nahin, 1988)
In this section, I will provide an extensive review of the uses of imaginary numbers and how they are manipulated in mathematics. The uses of imaginary numbers are most practical when used in terms of complex numbers. A complex number is simply a number that is represented with both a real and an imaginary part such as (a + bi) for any given integers a and b. The link above will provide an overview of complex numbers through explanations, videos, and worksheets.
The addition of complex numbers into the number system has greatly enhanced the types of problems that are solvable. When society finally caught on to the idea, many of the previously impossible problems became possible. In terms of application, the field of engineering is rich with examples where complex numbers are needed and helpful in accomplishing tasks. The link above will give a brief review of some of these difficult applications.
The link above provides a list of APA references for all of the information, pictures, and videos used throughout this webpage. Information is parenthetically cited within the text of the History, Explanation, and Significance sections, but the full citations will be provided here if you want to access more information on a given topic.
