00:00 Intro

00:14 Powers with complex numbers

01:06 Power definition in the real numbers

03:45 Using logarithm to write powers

04:50 Power definition in the complex numbers

06:05 What to do with a complex base?

07:00 Principal value of the power function

08:48 Credits

Q1: What is $i^4$?

A1: $i$

A2: $1$

A3: $-1$

A4: $-i$

Q2: What is $e^{i \pi}$?

A1: $1$

A2: $-1$

A3: $e$

A4: $0$

Q3: Consider the principal value of the power. What is $i^i$?

A1: $0$

A2: $\frac{\pi}{2}$

A3: $\exp \left( -\frac{\pi}{2} \right)$

A4: $\exp \left( i \frac{\pi}{2} \right)$