Anyone else give up on math as soon as complex numbers came into the picture?
I mean, it's literally the biggest cop-out I've ever seen. I thought math was supposed to be precise and realistic.
Now mathematicians can simply invent a whole set of numbers out of their asses just because nobody has come up with a good enough answer to some problems?
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uh no lmao
im an ace student in my pre-calc class.
just gotta try a lil harder, capiche?
alegebraically closed fields are really nice things.
>nobody has come up with a good enough answer to some problems?
oh but there is a BRILLIANT answer to those problems. it's called the the complex numbers.
I gave Up once math stopped being Numbers and became words
A REAL answer to those problems. Not some bullshit fabrication .
in which way are the real numbers more "real" than the complex numbers, besides the name ?
In what ways AREN'T they fake?
It's the reals that are pulled out from a hairy ass. Complex numbers would be ok if they were just pairs of rationals.
So i assume you don't do any geometry that isn't in a higher dimension than 3?
>simply invent a whole set of numbers out of their asses
the imaginary number comes from the quadratic equation
[math] x_\pm\,=\,\dfrac{-b\pm\sqrt{b^2-4ac}}{2a} [/math]
Honestly I hated complex numbers too and didn't see the point.
But I'm taking graduate complex analysis now and it's really interesting and powerful.
>out of their asses
there was a good reason
Every number is "fake", numbers don't exist in the real world. They're just an abstract concept. The real numbers, rationals, integers, they are just as "fake" as complex numbers. But they are good for describing and solving real world problems, so we use them. Honestly the only reason why you feel that "real numbers" are "real" is because of their name and the only reason why you feel that "imaginary numbers" are "fake" is because of their name.
how?
I don't agree with that.
I think numbers are indeed very real concepts.
As a testament to their realness, we can not only record and keep track of physical objects with them, but we can also use them to predict distant real-world phenomena centuries before they happen. We can calculate the trajectory of projectiles, and how long they will take to reach their minimum/maximum.
Now try recording things with complex numbers.
If complex numbers are real, then it's probably not in our plane of existence.
If your answer to a mathematical problem isn't a natural number or some conclusion derived from the properties of natural numbers, then it isn't a "real" solution.
What the fuck is pi? Repeating numbers? Are you fucking kidding me?
>Anyone else give up on math as soon as complex numbers came into the picture?
Yes, unfortunately such ignorance is quite common.
Integers, rational numbers, real numbers, and complex numbers are all derived from properties of the natural numbers, via increasingly elaborate abstractions.
Sounds like the real problem is that you are seemingly unable to deal with abstractions beyond a certain point.
Things that can happen thanks to complex numbers:
Vibration and Damper models
RC/RL circuit analysis
Solution to Second and higher order ODE's
Solution to PDE's
Analyis of literally anything even remotely resembling a wave or cycle with a phase
Linkage analysis, which is cumbersome and slow without using Euler's Formula
And many more. I am far from an expert on any of these fields let alone the ones I couldn't list - and it is abundantly clear that you are nothing short of a total idiot
I'm not a total idiot.
I'm pretty ignorant when it comes to math. I know there's a great deal I have yet to learn, so I wanted to spark up a conversation so I can learn something.
No one replies to my threads whenever I don't act like a presumptuous/pretentious asshole.
Fully represent pi as anything other than the symbol, m8
Technically, anything passed 30 or something decimals is irrelevant because there is a limit to how small you can get.
You can calculate the circumference of the observable universe down to the nearest hydrogen atom with 20 or so decimal places
let me guess, you're an high school dropout?
>an high school dropout
No
Math isn't supposed to be "realistic" as it's not science, when mathematicians come up with new things in math they're usually trying to keep consistent with what has already been established
if 4ac is greater than b^2.
>record and keep track of physical objects with them
>Now try recording things with complex numbers.
so let's start from the beginning. natural numbers represent how many apples I have. rational numbers represent how to split the cake. real numbers represent how long is the stick. complex numbers represent how much I turned the wheel. I don't see what's the problem here.
Well isnt it possible that the more we are substituting our own language of math into a real life problems that we could possibly be just simplifying real world problems with whatever puzzle we can make to make sense of this problem?
If that's the case, then Complex Numbers naturally model systems that rotate, scale, or oscillate. A simple to understand example would be a damped spring. You see them come up in electrical engineering constantly, also, and functions of a complex variable have some nice properties that Real functions simply don't. You'll learn more about this as you get further in your studies, especially if you're going into engineering. Good luck.
You think imaginary numbers are creative? Just wait until you get to functional analysis and where they come up with generalizations to measurability itself by generalizing operations to any set of objects.
The only constant theme in mathematics really, is that it forever gets more difficult.
Try looking into signals and systems/phasor analysis. I'm an EE and that shit is a godsend
christ I wish that people would stop being so enamoured with the fact that they're called "imaginary" numbers
they have so many uses and the second that people hear the name "imaginary" they think that math has no use