this post was submitted on 02 Mar 2024
782 points (95.8% liked)
Science Memes
11243 readers
2879 users here now
Welcome to c/science_memes @ Mander.xyz!
A place for majestic STEMLORD peacocking, as well as memes about the realities of working in a lab.
Rules
- Don't throw mud. Behave like an intellectual and remember the human.
- Keep it rooted (on topic).
- No spam.
- Infographics welcome, get schooled.
This is a science community. We use the Dawkins definition of meme.
Research Committee
Other Mander Communities
Science and Research
Biology and Life Sciences
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- !reptiles and [email protected]
Physical Sciences
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
- [email protected]
Humanities and Social Sciences
Practical and Applied Sciences
- !exercise-and [email protected]
- [email protected]
- !self [email protected]
- [email protected]
- [email protected]
- [email protected]
Memes
Miscellaneous
founded 2 years ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
Is there much beyond i^2 = -1, z = a + bi, and e^iθ = cosθ + isinθ? I didn't think the extended cinematic universe was that big...
You can literally take a class on Complex Analysis. Turns out that those "small" modifications have huge ramifications. They add a ton of extra structure to the real numbers which can be exploited, particularly if your problem can be expressed in terms of sines and cosines, or if your problem lives on a plane.
For example, complex differentiability is much more stringent than real differentiability, to the point that the existence of one complex derivative implies the existence of all of them! Furthermore, you have to be really careful extending the classic functions to the complex numbers. Typically, you either end up with a multivalued function, or you have to pick a specific branch that is single-valued.
If you want to learn more, Theodore Gamelin's Complex Analysis book is a good place to start. But to read it, you'd really benefit from a background in vector calculus. For a more "practical" but still detailed account of complex variables, check out Complex Variables and the Laplace Transform for Engineers by Wilbur LePage, which just assumes basic calculus.
What does electric current "i" have to do with the glorious imaginary unit j ?
This post was brought to you by Electrical Engineering Gang.
Good to see a fellow J enjoyer.