Ludwig Beilschmidt

Complex numbers have no logic.

, 17th September 2012 at 09:16 PM (168 Views)

Today, we started on complex numbers in Algebra 2. Specifically working with √-1, which is represented by i. Then she went on a tangent about how (√-x)^2 =-x. However, my friend and I found a problem in that that no one noticed. We asked to show the problem on the board, as follows:

(√-1)^2 = √-1 * √-1 = √1 = 1. A negative times a negative is always a positive. In the words of Katt Williams, 'Yes, every time.' However, the teacher countered with a statement that in the complex number system, which is entirely different from the real number system, that's not true. On the other hand, the students wouldn't shut up about how my friend and I made a new theorem, so to speak. Bitch please, that's 4th grade math.

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Comments

MegaChar - 18th September 2012 01:51 PM
I have never been any farther then Geo class so this look like trying to figure out Pokemon battles but ill get on topic.

yeap... - * += - and vice versa ...Im in a Algebra 1 class and I noticed that some people have problems when it comes to negative and positive numbers,I don't but somehow lots of people don't get that very much...But again, your one level higher Algebra class then I am so I might be wrong.
TheMissingno. - 18th September 2012 01:54 PM
@Pokémon Trainer Calvin;

√-1 * √-1 = √1

^This statement is false. √-1 * √-1 = -1.

Your problem is that you're assuming "√-1" is a negative number, which it is not. You're also multiplying exponents incorrectly. remember that √x is a different way to write x^1/2.

Think about it this way. if you have -1^1/2 x -1^1/2, you get -1¹, which is just equal to -1.

Updated 18th September 2012 at 02:01 PM by TheMissingno.
H-con - 18th September 2012 02:05 PM
They have a perfectly fine logic, but you should start looking at them as vectors in the complex plane. Makes things much more obvious, at least if you ask me.
TheMissingno. - 18th September 2012 02:07 PM
@H-con; I think he's in middle school...
H-con - 18th September 2012 02:10 PM
Originally Posted by TheMissingno.

@H-con; I think he's in middle school...

Yeah... Shame though, if you ask me that notation makes things much more understandable.

Fly, my vectors, fly!
TheMissingno. - 18th September 2012 02:20 PM
Yeah, it's probably too early for him to learn about complex numbers anyway, since he doesn't know vectors and things like this blog can happen. I guess it's good to know that they exist though.
Ludwig Beilschmidt - 18th September 2012 02:47 PM
Actually, I'm a high school junior, and we're just learning this stuff. Thanks for clearing that up, by the way. Because I thought that negative numbers didn't have square roots, because no number squared equals a negative number.