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.
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 UA-cam for a more structured approach. Hope this helps :)
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.
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!
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.
![The Most Useful Curve in Mathematics [Logarithms]](/img/n.gif)
Am I the only one who thinks the animation style resembles 3blue1brown? Keep up the good work man!
Thank you so much
Xander Gouws, are you alive and kicking? If not, rest in peace and thank you for your contributions.
@@pinklady7184 what
Love it! Short, crisp, clean, and clear!
You deserve more recognition, man ♥️
Thank you so much ❤😘
So this is how Pure Mathematicians developed the construct of a Complex Logarithm Mapping. Maybe this is the process that Euler used.
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.
This channel's gonna blow in 3,2,1...
Wonderful video! Great amimations and a calm voice! Thanks a lot!
Perfect explanation!
Brilliant solution. Thanks for tutorial.
Hey man! Can you tell me what is the name of the font that you are writing with, it looks really scientific and awesome?
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 UA-cam for a more structured approach.
Hope this helps :)
@@XanderGouws Thank you for your help :)
The complex definition of sine and cosibe is no the same McClaurin Series as always?
😊very clear! Brilliant!
Very good video.
Understood the complex log in less than 2 minutes. Skipped a bit a head :P
Very much appreciated.
I'm glad I could help :D
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.
Thank you so much! I'm glad I could help :)
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
6:43
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?
π = ln(-1)/i
π = iπ/i
π = π
🤷
0:27 “This isn’t because the values don’t exist, but because they’re not real.” Hmmm okay mister
Why didn’t you mention arg (z)?
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.
شكراً جزيلاً 🤍
(1 + 2n)Pi*i, where n is an integer?
U R amazing!
What is 2+2?
7
first you divide by zero on each side
Loved it
Letting the log have multiple values doesn't break the math.
why did this channel stop its another one of those gold math channels like 3b1b
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!
θ=π/4 , r^2=1^2+1^2 , k=0 , i*π=4*ln(1+i)-2*ln(2)？
0:38 this identity isnt actually eulers but still but the TRUE eulers identity is (sigma n=1 to ∞) (1/n²)=π²/6
ln (-1) = error
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...)
Love it
314 likes :D Love it
ln (-1) = undefined
Dude if you tried on an calculator ofc it will not work
#ln #naturallogarithm #logarithm
Oh boy
Kindly speak allowed and in a slow paced way for non- natives.
😮
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.
Плиз нот туркиш
Го руссиш
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.
He specifically addresses this if you keep watching...
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