Imaginary numbers are a meme

Imaginary numbers are a meme

I mean, they kind of are.

They are. They're only useful in acoustics, QM, and DSP. Aka: the biggest memes to ever be created.

Thanks for clearing that up.

Language is a meme.

memes are a meme

>be on sci
>use scientific jargon term in slang sense

>complex analysis is a meme
that's actually true

Imaginary "numbers" is a misnomer because they are not numbers.

Still pretty useful though

>acoustics
how?

Alright, prove to me that pi is transcendental without using complex analysis.

signal processing uses complex numbers mhiy dhude

Acoustics deal with sound. Which are waves. Litearlly anything with waves deals with imaginary numbers.

can you write down all the digits of pi?
>no
can you represent pi without self-reference?
>no
bam, transcendental

>> Studying for undergrad complex variables final exam
>> only seemingly useful application I've learned is residue theorem

>uses electricity
Shiggy

Imaginary numbers are necessary. They are a logical extension of numbers. Think Number.imaginary = square root of -number squared. It's not nothing.

... I need to read analysis god damn

why can't imaginary numbers be confined to the set of integers? Why must they be an extension of reals?

What exactly are imaginary numbers and what makes them "imaginary?"

I quit math after Calc 1.

What about when we use it to analyze real valued functions? e.g. using complex analysis to evaluate improper integrals, using complex analysis to analyze oscillating functions.

Doesn't sound like a meme to me, and you don't sound like you know much complex analysis

That's retarded.

What if I have an imaginary friend? He's not an actual friend of course because he doesn't exist. But we still call him an imaginary friend.

Yeah but that's what everything else built up to. You don't get the residue theorem for free.

So that we can solve x^2 = -2.

>sorry no latex

Where are imainary numbers used?
Calculus, Linear Algebra or Diff Eq?

sorry for asking a total noob question, haven't taken a college level math course yet.

numbers, in fact, are points in multidimensional space.
when we say "real" numbers, we actually mean points on single-dimensional space, the Re axis.
"imaginary" numbers is a second dimension, so complex numbers are in fact points on a plane - complex plane.
similarly, quaternions are points on four-dimensional space, and so on

>saying DSP is a meme
>on the internet
Oh the irony

In physics, for example, imaginary numbers are used to calculate complex impedance. Things like inductors and capacitors have reactance similar to how resistors have resistance. We can add up all of the resistance and reactance and take the real part as an answer. Its useful for making things more accurate with circuits.

Also things like sin(Φ) and cos(Φ) are defined in terms of i.

When people say they use imaginary numbers, what they really mean is that they use the complex representation of trigonometric functions.