Why Complex Numbers? (3 of 5: The Imaginary Unit)

[candiceford]

His class is so quiet. I makes me think he's not actually speaking to a real class. Real class or not, the best teacher I wish I had. For real!

[Slarti]

06:30 - genius, you remembered to reverse the direction of positive and negative numbers.
I think this is what makes you a great teacher, you are able to empathise with your audience.

[fkjsg]

...that perfect circle right at the beggining...

[xBobz]

Love how comprehensive your videos are.

[Decco]

I also wish American math classes gave historical context for a better appreciation of these kinds of things

[ttkummer]

good lord where was this guy when I was learning about complex numbers???

[vipin]

Awesome, I wish you would have existed as teacher 22 years ago.

[marcotrosi]

little correction about the Z and its German translation. Z stands for "Zahlen" which means "numbers". "zählen" lower case z and the ä Umlaut means "counting"

[ramamohammed-jsjs]

you are the teacher that I wish I ever had

[keypo]

lmao this is hilarious, i tried graphing x^2 and overlappping it with another function of x^2 + 1, there I just realized your point

[pepperonik]

What about 1=0.999...? There's two decimal expansions for (allegedly) the same number. Does that mean 1 doesn't fit the criteria for real numbers?

[theMagos]

We can't calculate -1^(1/2) so we just call it i and it works. How about we do the same for 1/0 and call it j? No more problems dividing by zero...

[cybervigilante]

Brown postulated Atoms. Brown's stupid cousin Bob said, "Magic." Nobody remembers Brown's stupid cousin, and it isn't called Bobbian Motion.

[Life-whwu]

Sir
i^0.5 =0.7 +i 0.7
Y can't it be -( 0.7 +i 0.7)

[KarlDeux]

Never write sqrt(-1)!!!
Because sqrt(a) * sqrt(b) = sqrt(a * b)
So like this, you have sqrt(-1) * sqrt(-1) = sqrt(-1 * -1), and -1 * -1 = 1
So when you write sqrt(-1) and you have it squared, you have 1 and no longer -1.
This is why the number i got used, not because i could mean "imaginary"

[leroyleon]

Let's do new imaginary numbers where i = 1/0