Intuition for i to the Power i - Lockdown Live Math

, 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..
Exponential function for i^i.
Question 1.
Plug-in imaginary number in exp(x) polynomial.
Answer 1 and explanation.
What it really means i^i?.
e^it as a position vector .
Question 2.
Audience question from twitter.
Answer 2.
Where you get after traveling π/2 units of time for position vector e^it.
Question 3.
Audience tweets.
Answer 3.
Question 4.
Answer 4.
How exp(rx) or b^x really works?.
Question 5.
Audience tweets.
Answer 5.
Visualization of f(x)= exp(r*x) i.e. e^(r*x), where r= unique complex number.
Questions to think about.
Audience tweets .
Power tower for i .