Hi team,

As many of you probably already know, I am a math student and one of the terms that I learned as a math student that really intrigued me was the concept of imaginary numbers.

The criteria of the assignment is then simple, you are to give three definitions of relatively complex term of your choice. The three forms of definition you are to give is then a parenthetical, sentence, and expanded form of the definition.

The main objective of this assignment is then to describe a technical term to an audience that has no previous knowledge of that field. This then means that there needs to be both an increase of detail when describing specific terms as well as the use of less technical wording when describing the term.

**Term: **

Imaginary Number

**Parenthetical Definition:**

An imaginary number is a number that is negative when squared.

**Sentence Definition: **

An imaginary number is a mathematical value in the form of ix, where x is a real number while i is the positive square root of negative one. Unlike other numbers, imaginary numbers are negative when squared.

**Expanded Definition:**

**How does it work ?**

Let’s imagine that you want to take the square root of a negative number such as negative nine. Normally this is impossible as most people are taught that you can not take the square root of a negative number, but this all changes with imaginary numbers. With imaginary numbers, you can split the square root of negative nine to the square root of nine multiplied by the square root of negative one. The square root of nine would be three and the square root of negative one is i so therefore the square root of negative nine is 3i.

**What are its parts ?**

An imaginary number is a numerical value that when squared is still negative. To get a better idea of how it works let’s break it down into its 2 main parts.

- Real number coefficient is the number in front of the imaginary unit i. The real number can be positive or negative.
- The imaginary unit or the variable i is equivalent to the square root of negative one and is usually placed behind the real number value.

**Visual Examples:**

**What is it not ?**

An imaginary number is not a fake or a made up value of some kind. Instead it is a quantifiable value that can even be graphed when combined with other real numbers.

**What are the applications of Imaginary Numbers ?**

Imaginary numbers are most useful when transformed into complex numbers. Complex numbers is then the combination of an Imaginary number with a real number. For example 3i + 4 would be a complex number. Complex numbers are then often used in fields such as electrical engineering and aerospace engineering.

**References:**

“Imaginary-Number.” *Imaginary-Number – Math Word Definition – Math Open Reference*,

https://www.mathopenref.com/imaginary-number.html.

*Imaginary Numbers*, https://www.mathsisfun.com/numbers/imaginary-numbers.html.

“What Is Imaginary Number? – Definition from WhatIs.com.” *WhatIs.com*, https://whatis.techtarget.com/definition/imaginary-number.

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