Types of Things #6

Imaginary numbers are numbers made using the imaginary unit i, which is defined as a solution for x to the equation x^2 + 1 = 0 - in other words, i is the square root of -1. You can treat it like a number in terms of adding and multiplying, so 3 * i = 3i, you can also have pi * i, or 2.234837i, etc. Those are all imaginary numbers. When you add them to real numbers, you get something like 3 + 4i, which is what's called a complex number. Despite the seemingly strange definition, they're actually incredibly useful and powerful in both mathematics in general and engineering.

Irrational numbers are those that can't be expressed as the ratio of two integers. So 2/3 is rational, -4234/7437 is rational, but pi and e are both irrational, along with most other numbers.

Imaginary numbers are formed using the imaginary unit i, which you can think of as representing the square root of -1. You can treat it like a variable when it comes to multiplying and adding with other real numbers, and get things like 2i, or pi * i, or 2347i/7108. These are all imaginary numbers. When you add a real number, like 3 + 4i, the result is what's called a complex number. They're incredibly widespread in mathematics and are very useful in some engineering fields as well.