@z3lop59

At 9:27 shouldn't the blue cos have an offset of 90°? like this it's two sin waves but not one sin and one cos.

@aromview

The level of care put into these videos is matched only by Spongebob tucking pickles under a cheese blanket and reading them a bedtime story.

@claytonmoore3869

Tibees is the person we all need. She's so relaxing and calm

@itsmemailingyou4234

Tibees is an imaginary friend for many people, while being real.

@fizyknaut8108

I remember finding out about imaginary numbers and being like "OK, cool... but why?" This explains it really well.

@mrbjjackson

I was taught imaginary numbers in a 3 year engineering degree, and also have watched a load of YouTube videos including the whole of the "Imaginary numbers are real" series and this is the first time I feel like I've got a grasp of why imaginary numbers work and are useful. It was your line about "imaginary numbers are good at describing circular motion" that really made things click. Als the 45° example. Thanks very much 🙏

@alpereng4652

I m an high school student in Turkey. Our educational system is all about rote learning and the curriculum is too overloaded.  This kind of videos ( logically explaining..) really helpful. Thanks a lot

@EayuProuxm

4:43, why is Tibees in the back?
Tibees: This is the negative real world

This is one of the greatest pieces of cinematography I've ever seen. Style and content perfectly fuse to produce meaning! This youtube video needs to be archived for future generations.

@chrisphistry5949

That really started to make sense! It's been over 30 years since I learned about imaginary numbers and only now are they starting to make any sense. More "Joy of Mathmatics", please and thank you.

@zanop15

That cat’s cuteness is  immeasurable! It’s just like trying to use a ruler to mesure the sqrt(-1)

@watsoncrick6071

ive studied imaginary numbers before but im pretty glad to say that I've gained a new perspective on this topic!! Thanks Toby!

@mohamedkhan5198

If you were my Math's teacher, I would be PhD mathematics today.

@maximillianwunderlich6179

That one dislike is from tibees... the cat accidentally clicked on the mouse

@RussellSubedi

This is my new favorite quote regarding imaginary numbers:
6:42 "Despite the name, they are not imaginary at all. Some people just have trouble seeing them."

@lostandfound3588

Watched this twice because of her voice, it's like she makes my brain feel my heart beat

@karora

I remember learning about imaginary numbers at high school, and thinking "what a waste of time". And then a few years later I was training as an electronics technician (late '70s), and learning that I had to use imginary numbers for waveguide engineering calculations.  Not so imaginary now, I thought!

@FirefoxGuy18

Your voice is very calm and soothing.It’s captivating and helps to make learning easy

@timothystockman7533

"We're sorry. You have reached an imaginary number. Please hang up, rotate your phone 90 degrees, and dial again."

@BlackHermit

Traveling back and forth between the real world and the imaginary world feels so wonderful! Thank you so much for providing us with these precious passports, Toby!

@learnmoreushe3678

I left the topics on imaginary numbers in my text book years back, untouched. Now they are courting me again. What a way to relax my mind, listening effortlessly to Tibees' genius teaching style. She's like Vivaldi piece, listening to her.