Intuition for i to the Power i - Lockdown Live Math

Intuition for i to the Power i - Lockdown Live Math

3Blue1Brown via YouTube Direct link

, 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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, 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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Intuition for i to the Power i - Lockdown Live Math

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  1. 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.
  2. 2 Exponential function for i^i
  3. 3 Question 1
  4. 4 Plug-in imaginary number in exp(x) polynomial
  5. 5 Answer 1 and explanation
  6. 6 What it really means i^i?
  7. 7 e^it as a position vector
  8. 8 Question 2
  9. 9 Audience question from twitter
  10. 10 Answer 2
  11. 11 Where you get after traveling π/2 units of time for position vector e^it
  12. 12 Question 3
  13. 13 Audience tweets
  14. 14 Answer 3
  15. 15 Question 4
  16. 16 Answer 4
  17. 17 How exp(rx) or b^x really works?
  18. 18 Question 5
  19. 19 Audience tweets
  20. 20 Answer 5
  21. 21 Visualization of f(x)= exp(r*x) i.e. e^(r*x), where r= unique complex number
  22. 22 Questions to think about
  23. 23 Audience tweets
  24. 24 Power tower for i

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