What are Complex Numbers?
An overview of the operations with 12 Examples
Did you know that Complex Numbers behave live vectors and have amazing similarities to algebraic operations?
A Complex Number is the sum of a real number and an imaginary number, and this lesson is all about how to represent, sketch, and perform algebraic operations with Complex Numbers in Standard Form.
While their name implies that they aren’t real, let me tell you that they are, and they are incredible powerful – especially when they are combined with real numbers to form Complex Numbers.
Wait a minute, you mean we can take the square root of a negative number?
Yes and No.
While it’s true that we can’t take the square root of a negative number; the square of a negative number (two negative numbers being multiplied together) is always positive, we can separate the Imaginary Number from the Real number, thus forming Complex Numbers.
In fact, imaginary numbers and Complex Numbers are amazing in the way they help us solve quadratic equations and differential equations, as well as how we explain real-world phenomena in such disciplines as electrical engineering, physics, and economics, as Math is Fun accurately points out.
So, we start of this video with a quick overview of imaginary numbers and how they help us to form Complex Numbers.
Next, we learn how Complex Numbers are similar in nature to Vectors, in how we graph them on the Complex Plane, with both real (horizontal) and imaginary (vertical) components, as nicely stated by Khan Academy.
Then we learn how to represent a Complex Number in Standard (Rectangular) Form, and how to perform basic operations such as addition, subtraction, multiplication and division using our beloved Conjugate.
Complex Numbers in Standard Form Video
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