ITT: We shit on Complex Numbers

top notch

They're good numbers, Brent.

They make circuits easier
I LOVE them, I wouldnt KNOW how I could LIVE without those BADboys

>complex numbers
>not the set of polynomials with real coefficients modulo x^2+1

For the love of god, can anyone remind me what two angles of the same degree are called? Like pi/2 and 5pi/2? Both 90 degrees even though they're different angles. Not colinear, right?

>haha look I phrased something in slightly more complicated terms! I'm smart!

Alright Veeky Forums retard here.

Why is the square root of negative 1 so important? I just dont fucking get it.

Every non-constant polynomial with coefficients in R has a root in R+iR.

In phase?

How would you explain that to a 12 year old?

Gas yourself OP you shitcunt

Simply put, it's important because it's useful.

Imaginary numbers are a natural extension of the real numbers like negative numbers are for the whole numbers.

How Can Mathematics Be Real If Our is Aren't Real?

It's quite miraculous. The fact is that adding a little more wiggle room is useful, even for questions purely about real numbers. For instance, why is the radius of convergence for the Taylor series of 1/(1+x^2) at 0 so small? It's because of the complex root in the denominator.

fuck you and your eyebrows and everyone who lives in your inverted venomous marsupial-infested jail continent

i wish flat earth was real so your whole fucking people would be cast into space as the planet rotated

>R

Huh? Isn't it the same radius as 1/(1-x), I.e. 1?

Yes..why would you expect that? Those are two completely different functions. Look at the graphs -- notice how one blows up and one doesn't?

The completion of Q w.r.t |.|

It doesn't exist

Every metric space has a completion.

Not if it's infinite, infinite sets don't exist because they are counterintuitive

>literally just fucking transformations from R^2 to R^2
>anything substantial

lmaoing at your life complex numbers

You could say something to this effect about anything in math. Having different viewpoints on an object is a blessing.

except I was just being retarded bro, there is no equivalence.

off yourself, brainleto

Congrats, I guess.

What the fuck did you just fucking say about complex numbers, you little bitch? I’ll have you know I stopped caring about math when I was introduced to the concept of imaginary numbers, and I’ve been involved in numerous secret raids on Al-Gebra, and I have over 300 crocks of shit. I am trained in equations that can only be solved by inventing numbers that can't exist and I’m the top math deity in the entire US academic forces. You are nothing to me but fucking wrong. I will wipe you the fuck out with math the flaws of which have never been seen before on this Earth, mark my fucking words. You think you can get away with saying that shit to me over the Internet? Think again, fucker. As we speak I am contacting my secret network of algebra solutions across the USA and your IP is being traced right now so you better say "the correct answer is whatever the correct answer is", maggot. The math that says the pathetic little thing transcribed to words. You’re fucking dead, kid. I can be anywhere, anytime, and I can mark you wrong in over seven hundred ways, and that’s just if you write it down in english instead of ancient math runes. Not only am I extensively trained in unarmed combat, but I have access to the entire arsenal of the United States Logical Math Corps and I will use numbers that never lie to their full extent to wipe your miserable ass off the face of the continent, you little shit. If only you could have known what unholy flaws your little “clever” human construct was about to bring down upon you, maybe you would have held your fucking tongue. But you couldn’t, you didn’t, and now you’re paying the price, you goddamn idiot. I will shit complex numbers all over you and you will drown in it. You’re fucking dead, kiddo.