Imaginary numbers and complex numbers interest me a lot. Aside from the properties of infinity (), complex numbers are, well… complex! They’re very strange and yet they open a whole new world of numbers beyond the Real numbers .
Let’s find out what real numbers and complex numbers are.
- The Real numbers are the set made up of all the Rational numbers and Irrational numbers together.
- To make our transition into the complex numbers, we need to define what is since it is not a real number. That is to say, there is no real number so that when we square it, it is equal to , (). So we make up a new number to make it work. We define the Imaginary unit, to equal , (.
- An Imaginary number is a specific kind of complex number written in the form where is a real number and is the imaginary unit.
- The Complex numbers are the set that involves a combination of real and imaginary numbers. They are written in the form , where and are real numbers.