Complex Variables - Lesson 001 - Crazy Intro to Complex Numbers
So, I'm at work with about half an hour until they kick me out (and they haven't given me any more tasks to do, so I can actually post this~)... I guess it's about time to do one of those belated math posts I promised, right? Recall from those old, bygone days of College Algebra when you were told you cannot take the square root of a negative number. And then a few days later, your book/teacher/whatever proceeded to tell you that YES, YOU CAN. This square root of a negative number does something funny though. It's no longer a "real" number. It's an imaginary one. I know, math people just like to make crap up all the time just to mess with your head.
You can do any basic mathematical operation you ever learned on these babies. Add, subtract, multiply, divide - do it all.
Before we get too much further, let's test out some of these concepts.
√(-4) = 2i Remember that the square root of 4 is 2, but because this is the square root of -4, we tack on an "i" to our result.
√(-4) + √(-36) = 2i + 6i = 8i √(-4) + √(36) = 2i + 6 ≠ 8i Recall that you can only add "like terms" - constants can be added together, terms with x's can be added together, terms with squared-x's can be added together, etc. The same applies to terms with "i's".
The result 2i +6 is actually called a "complex number" because it involves both a real value and an imaginary value added together. This is where we get the term "complex variables".
This post is so messy, but I promise these posts will get better and become more cohesive as we go. If you have any questions, please ask!