Imaginary number

>imaginary number
>is a letter
why?

It's not a letter, it's an imaginary unit.

It's a hassle to write root(-1) for every imaginary number, and so i is neater and easier.

>literally does not exist
why bother then?

The letter just represents the concept. There doesn't have to be anything intrinsically "imaginary number-like" about a letter on a piece of paper for it to stand for imaginary number.

we already used up all the numbers to make the reals. It's just a placeholder till we find more numbers

regular numbers don't exist either

>why are constants represented by letters/symbols?

>Veeky Forums - Biting late night baits since 2010

Pic related is 33 kilobytes. You can count the kilobytes, one, two, three, so on and so forth. You can't have i of anything.

ok but what happens when you want to find like idk how many pixels the image has when you scale it
and then like there's an imaginary number involved

or like circles and shit

I have i girlfriends

you win

Okay, but what are numbers? You're looking at it too much from a practical aspect, rather than an abstract POV.

Numbers are a way for us to precisely describe things. If I told you A was equal to A amount of goods.

Consider this, if we weren't use the decimal system and maybe we were using a number system, such as the hexadecimal number system. Where A1 is equal to 161 amount of things.

The reason I keep saying things is because this is why we developed math. We start using mathematics to describe abstract forms precisely, we used it to precisely describe the quantity of the goods we had to sell and the cost of said goods. What is 1? It's a number we made up, 1 could literally have been a letter, a symbol for all we care.

besides, sqrt(-1) isn't entirely accurate anyway

but that's not correct, [math]\sqrt{-1}=\pm i[/math]

"Imaginary" is a misnomer, they're actually "complex" numbers.

They're the imaginary parts of a complex numbers

it is. either works.
sqrt(-1) means you pick either one and stick to that choice. they're literally the same

Kilobytes aren't numbers.

Isn't the radical symbol used commonly/conventionally for principal (square) root of a number?
Wouldn't that make your equation unintelligible by convention, since principal square root does not give negative and positive result?

i^2 = -1 is all we know
sqrt is a kludge in this case

>imaginary number
>it's not a letter, it's an (((imaginary))) unit
Change that to lateral unit and you will please my autistic frustration with a name given to something which is not imaginary as any other number in mathematics and shows up in physics and engineering all the time

a complex number is a number with both real and lateral units, complex numbers are written as a+bi for a reason, the bi part is a lateral unit, not a complex number

"i" is just a symbol used to denote a specific element of C (the collection of all complex numbers). in the exact same manner as "1" is a symbol used to denote a distinguished element of natural numbers, namely the only number satisfying 1*x = x for any non-zero x, and for example "5" is just a symbol used to denote another element of natural numbers, namely the number 1+1+1+1+1

By convention doesn't the radical symbol refer to the positive root

Aren't they only complex if you add a real number to i?