The Complex Logarithm

In this video, we cover three central ideas: the natural log of -1, the natural log of any complex number, and the principal log.

I know it's been a while since I've uploaded a video, but I'm now done with high school! Since I'm only starting university in September, I've got a lot of free time to work on more videos. I'm going to try to upload every two (plus or minus 1) weeks.

[Christian-qhzu]

Am I the only one who thinks the animation style resembles 3blue1brown? Keep up the good work man!

[MathManMcGreal]

Love it! Short, crisp, clean, and clear!

[るるん-nn]

Awesome video!

Note: The domain shown at the end isn't really standard, because you can't define a continuous version of Log on all of C. If you make both inequalities at 3:26 sharp, it will become holomorphic, which is much nicer in proofs and calculations.

[mathematicalmuscleman]

So this is how Pure Mathematicians developed the construct of a Complex Logarithm Mapping. Maybe this is the process that Euler used.

[shreerampetkar]

Wonderful video! Great amimations and a calm voice! Thanks a lot!

[armandoski-g]

This channel's gonna blow in 3, 2, 1...

[pinklady]

Brilliant solution. Thanks for tutorial.

[Labroidas]

Very nice video, well prepared, everything brought to the point in a simple way, and the visualizations are very clean and easy to follow. This video must have taken a long time to make in relation to how short it is! This makes it a lot easier to digest the tons of information in my textbook, thank you very much.

[PIPuniverse]

Hey man! Can you tell me what is the name of the font that you are writing with, it looks really scientific and awesome?

[engelsteinberg]

The complex definition of sine and cosibe is no the same McClaurin Series as always?

[antman]

Very good video.
Understood the complex log in less than 2 minutes. Skipped a bit a head :P
Very much appreciated.

[elreturner]

This always seemed obvious logarithms are just roots for when x is the exponent instead of the base just like square root of -1 except a bit fancier

[TheOriginalDeaf]

e^(I*pi) = -1
Ln both sides
Pi*i = ln(-1)
Pi = ln(-1)/i
I proved that pi is rational in the complex plain, is this true or did I do a wrong step?

[bebarshossny]

why did this channel stop its another one of those gold math channels like 3b1b

[РайанКупер-эо]

Letting the log have multiple values doesn't break the math.

[高木清治]

θ=π/4, r^2=1^2+1^2, k=0, i*π=4*ln(1+i)-2*ln(2)？

[abhishekdixit]

For z=a+ib

And


(If i'm right...)

[Effect_channel]

0:38 this identity isnt actually eulers but still but the TRUE eulers identity is (sigma n=1 to ∞) (1/n²)=π²/6

[redpepper]

0:27 “This isn’t because the values don’t exist, but because they’re not real.” Hmmm okay mister

[anwarh.joarder]

Kindly speak allowed and in a slow paced way for non- natives.