The Complex Logarithm

[@Christian-qh5zu]

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

[@XanderGouws]

Thank you so much

[@pinklady7184]

Xander Gouws, are you alive and kicking? If not, rest in peace and thank you for your contributions.

[@anjamoro8384]

@@pinklady7184 what

[@salmanshahriar5974]

You deserve more recognition, man ♥️

[@XanderGouws]

Thank you so much ❤😘

[@MathManMcGreal]

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

[@mathematicalmuscleman]

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

[@るるん-n6n]

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.

[@armandoski-g]

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

[@shreerampetkar5221]

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

[@mathsfamily6766]

Perfect explanation!

[@pinklady7184]

Brilliant solution. Thanks for tutorial.

[@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?

[@XanderGouws]

Hey! I believe the font I'm using here is just the default LaTeX font, which is Computer Modern. If you're not familiar with LaTeX, it's a markup language that lets you write math equations pretty easily. A great way to learn it is to play around with it using www.codecogs.com/latex/eqneditor.php but there are also some great tutorials on KZbin for a more structured approach. Hope this helps :)

[@PIPuniverse]

@@XanderGouws Thank you for your help :)

[@josemartinho424]

😊very clear! Brilliant!

[@prediccionescountryballs893]

6:43

[@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.

[@XanderGouws]

Thank you so much! I'm glad I could help :)

[@engelsteinberg593]

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

[@rattyoman]

damn, 5 years and still a banger

[@lamaiyad9596]

شكراً جزيلاً 🤍

[@antman7673]

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

[@XanderGouws]

I'm glad I could help :D

[@duckymomo7935]

Why didn’t you mention arg (z)?

[@XanderGouws]

It was easier to write θ than to use arg(z) every time - but maybe I could've made a note of it or something.

[@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?

[@Cyrenalux]

π = ln(-1)/i π = iπ/i π = π 🤷

[@elreturner1227]

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

[@ycombinator765]

Loved it

[@REEMAN_]

U R amazing!

[@bobsno1fan783]

What is 2+2?

[@rot6015]

7

[@n019n]

first you divide by zero on each side

[@redpepper74]

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

[@ZombieLoverPlays]

Love it

[@JDC2890]

(1 + 2n)Pi*i, where n is an integer?

[@bebarshossny5148]

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

[@XanderGouws]

My bad! I've been busy with uni recently and haven't had much time to put towards making videos :( I do plan to get back to it as soon as I can though!

[@yondabigman4668]

Oh boy

[@РайанКупер-э4о]

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

[@theophonchana5025]

#ln #naturallogarithm #logarithm

[@pucek365]

314 likes :D Love it

[@sarkarsubhadipofficial]

😮

[@theophonchana5025]

ln (-1) = error

[@theophonchana5025]

ln (-1) = undefined

[@soccerbels7947]

Dude if you tried on an calculator ofc it will not work

[@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

[@高木清治]

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

[@abhishekdixit638]

For z=a+ib cos(z)=[cos(a)cosh(b)]-i[sin(a)sinh(b)] And sin(z)=[sin(a)cosh(b)]+i[sinh(b)cos(a)] (If i'm right...)

[@anwarh.joarder8644]

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

[@otonanoC]

I waited and waited for the narrator to say that f(z)=ln(z) is literally the inverse function of f(z)= e^z . But he never got there.

[@ЕвгенийСимонов-к5о]

Плиз нот туркиш Го руссиш

[@pratyaksh1729]

Actually your result is wrong. Logarithm of a negative value is a multivalued function. That means it can have multiple values. For example: 3i*pi is also a solution.

[@1495978707]

He specifically addresses this if you keep watching...

[@theophonchana5025]

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