3 ms·
I think you need to study the Euler equation to understand the relationship between goniometric functions and exponential functions when calculating with comple
by nuancebydefault 4y ago
I think you need to study the Euler equation to understand the relationship between goniometric functions and exponential functions when calculating with complex numbers. One easy to remember formula that connects those functions.
- rectang 4y agoIndeed. The title of that 3Blue1Brown video is, “What is Euler’s Formula actually saying?” That “easy to remember” formula had been presented to me countless times. It only made sense once I stopped thinking about it in terms of repeated multiplication.
- l- 4y agoThe repeated "many folding", which would be better visualized as tendition, exponentiation ("tendaddition") pattern also breaks with fractions & at the most basic negative numbers: https://www.youtube.com/watch?v=mvmuCPvRoWQ&t=922s https://www.youtube.com/watch?v=mvmuCPvRoWQ&t=922s Also: https://news.ycombinator.com/item?id=28524792 https://news.ycombinator.com/item?id=28524792 "log base" would be better named untendaddition similarly division - does not necessary "separate" - untendition & unaddition - does not "draw under". Etymologos to use "given" symbols over the datum names.
- l- 4y agoFurther, the pattern matched "grouping" definitions (https://news.ycombinator.com/item?id=25278021 https://news.ycombinator.com/item?id=25278021) names have a better correspondence to the Greek scheme: diation, triation, tetration... while the "Group theory" definitions scheme lending to various geometries (hypercomplex: complex::hyperbolic, split-complex::elliptic, dual::parabolic) would match some other naming scheme.