The fascinating case of the complex logarithm 

I think dealing with inverse function in the complex world is one of the hardest things that look/should be easy In the future are you planning to make a video on Lambert w function If you are I would like you to talk between the relationship between deferent branches All I know that the relationship isn't linear like other famous inverse functions

2:10 I struggeld shortly with the derivation, noting that |w| = |e^z| = |e^(x+iy)| = |e^x| * |e^iy| = |e^x| should be correct and not e^x. But since the exponential of a real number is always positive, we can omit the absolute value bars, and indeed |w| = e^x. Sounds trivial but it got me for about 5 minutes.

Very good explanation- great👍

Thicker branch cuts in the future, pls. Thank you 🤝

16:45 What if a wasnt real number ?