What is Euler's formula actually saying? | Ep. 4 Lockdown live math
What does it mean to compute e^{pi i}?
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Beautiful pictorial summary by @ThuyNganVu:
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https://twitter.com/ThuyNganVu/status/1258220541686628353
Not on the "homework" to show that exp(x + y) = exp(x) * exp(y). This gets a little more intricate if you start asking seriously about whether the series really converge, what they converge to, and how exactly you define a…
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Chapters (27)
Welcome
0:20
Ending Animation Preview
1:15
Reminders from previous lecture
3:30
Q1: Prompt (Relationship with e^iθ=…)
5:40
Q1: Results
7:15
WTF, Whats The Function
10:00
Exploring exp(x)
11:45
Exploring exp(x) in Python
14:45
Important exp(x) property
15:55
Q2: Prompt (Given f(a+b) = f(a)f(b)…)
17:30
Ask: Which is more interesting, special cases or the general case
20:00
Q2: Results
23:50
Will a zero break Q2?
25:40
The e^x convention
27:10
Q3: Prompt (i^2 = -1, i^n = -1)
27:45
Ask: Zero does not break Q2
30:20
Q3: Results
31:05
Comparison to Rotation
33:00
Visualizing this relationship
36:50
The special case of π
39:20
Periodic nature of this relationship
39:40
Q4: Prompt (e^3i)
41:35
Q4: Results
43:55
Explaining the celebrity equation
45:55
Homework / Things to think about
49:15
Ask: Zero does break Q2.
50:30
Closing Remarks
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