Why do trig functions appear in Euler’s formula? This was the question I had when I first saw Euler’s formula. This connection between trigonometry and exponents seems so unexpected, especially along with complex numbers. To answer this question, we must journey into the intricate and beautiful mathematical relationship between trig functions, e, and complex numbers. We will look at two different ways to approach this question: one using dynamics, geometry, and the complex plane, and the other using Taylor and Maclaurin series. Both are equally fascinating, and both reach the same, amazing result by using a lot of beautiful math.
0:00 - Intro
0:38 - Unit circle on complex plane approach
7:30 - Taylor and Maclaurin series approach
12:39 - Conclusion
Additional Resources:
Geometric proof of the derivatives of sin(x) and cos(x)
1 view
10
1
1 month ago 00:03:07 1
Two Faced (Official Music Video) - Linkin Park
1 month ago 00:00:32 1
…but the people are retarded
1 month ago 00:08:10 1
AI Agents Will Create MILLIONAIRES in 2025 – Are You Ready
1 month ago 00:03:02 1
SPX Options Trading : Strategies for Big Gains!
1 month ago 00:02:41 6
sinking in the deep || Viktor (Arcane)
2 months ago 00:25:19 1
Существа в открытом космосе возможны? / Большой Взрыв наоборот / Астрообзор #169
2 months ago 00:00:59 1
Melania Trump is doing things differently this time
2 months ago 00:03:57 1
Don Toliver - BROTHER STONE (FEAT. KODAK BLACK) [Official Music Video]
2 months ago 00:04:04 5
Mass Effect Trilogy Trailer
2 months ago 00:02:49 1
Chris Isaak ~ Black Flowers
2 months ago 00:39:19 1
Historian Answers Witchcraft Questions | Tech Support | WIRED
2 months ago 00:04:45 1
Hollywood Undead - Hollywood Forever (Official Music Video)
2 months ago 00:03:13 2
Benson Boone - Beautiful Things (Official Music Video)
2 months ago 00:02:52 3
The Crying Game - Marcus Nimbler
2 months ago 00:04:38 1
Starbomb - Kiss The Elden Ring (Official Music Video)
2 months ago 00:23:07 1
Do You Know who You Are? | Bob Proctor
2 months ago 01:16:30 1
#1 Neurosurgeon: How to Manifest Anything You Want & Unlock the Unlimited Power of Your Mind
2 months ago 00:39:35 1
He QUIT CHESS for college, now he’s TOP 8! WEI YI Podcast
2 months ago 00:03:05 1
Jeorgia Rose - Undertone (Official Music Video)
2 months ago 00:01:39 1
Put 1 Cork in the Fridge and WATCH WHAT HAPPENS💥(Genius Trick)🤯
2 months ago 01:01:41 1
WildCraft Arena | BabyPunchers vs DANGE’s team | 3v3, 2v2
2 months ago 00:13:40 1
Why Didn’t I Know This Sooner! This 60-Year-Old Plumber’s Brilliant Idea Will Save You Millions
2 months ago 00:06:02 1
Youtube Unsubscribe from channels on autopilot with iMacros