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, when changing r to equal 0.69*i, I said "this is what we might think of as (2i)^x", but that is not correct. It's what we'd think of as [Exp(ln(2)*i)]^x for whatever complex number Exp(ln(2)*i) is.
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Exponential function for i^i
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Question 1
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Plug-in imaginary number in exp(x) polynomial
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Answer 1 and explanation
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What it really means i^i?
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e^it as a position vector
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Question 2
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Audience question from twitter
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Answer 2
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Where you get after traveling π/2 units of time for position vector e^it
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Question 3
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Audience tweets
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Answer 3
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Question 4
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Answer 4
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How exp(rx) or b^x really works?
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Question 5
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Audience tweets
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Answer 5
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Visualization of f(x)= exp(r*x) i.e. e^(r*x), where r= unique complex number
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Questions to think about
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Audience tweets
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Power tower for i
Description:
Explore the concept of i to the power of i in this comprehensive video lecture from the 3Blue1Brown series. Dive deep into the exponential function for i^i, understand its real meaning, and visualize e^it as a position vector. Learn how to plug imaginary numbers into exponential polynomials and grasp the intricacies of exp(rx) and b^x. Engage with interactive questions, audience tweets, and detailed explanations throughout the session. Discover the visualization of f(x) = exp(r*x) where r is a unique complex number, and ponder thought-provoking questions about power towers for i. Benefit from a structured timeline, beautiful notes by Ngân Vũ, and references to related videos for a thorough understanding of this complex mathematical concept.

Intuition for i to the Power i - Lockdown Live Math

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1 , when changing r to equal 0.69*i, I said "this is what we might think of as (2i)^x", but that is not correct. It's what we'd think of as [Exp(ln(2)*i)]^x for whatever complex number Exp(ln(2)*i) is.