REAL rotations within IMAGINARY numbers! #shorts

#shorts #short #comboclass #imaginary #imaginarynumber #imaginarynumbers #number #numbers #negative #positive #math #maths #mathematics

Combo Class is a crazy educational show where you can have fun learning rare things about math, science, language, and more! This is the SHORTS channel for faster-paced videos. Make sure you're also subscribed to the main Combo Class channel where full episodes go!

DISCLAIMER: any use of fire, tools, or other science experiments in this series is always done in a safe and professional way. Do not try to copy any actions you see in this series yourself.

[zedzedder]

So, is this "i" in the room with us?

[Dr.farazalam]

What's the saddest part in High School Math is the label "imaginary" given to a set of numbers that are very real.
- a doctor

[servvo]

"that's where i, the square root of -1 comes in"
woah i didn't know you were a number that's crazy

[toughenupfluffy]

Rene Descartes named imaginary numbers, ridiculing them as being 'fictitious.' He also claimed that animals were just machines that couldn't possibly have feelings.

[crazysasha]

That's a great way to put for people who don't know about/understand complex numbers.
But what you didn't mention is using the exponent of imaginary numbers to get a rotation by every angle possible.

[SuperMaDBrothers]

A way to see what squaring does. if z=x+iy, z^2=x^2 - y^2 + i 2xy. If z is closer to real, it ends up real positive. And if it is closer to imaginary, it ends up real negative. And if it has both x and y components, it ends up imaginary. So only the axes square to real. Pretty cool right

[troyyoung]

Imaginary numbers. I really love them. They are so simple yet so complicating, and so powerful. there is a subtle difference in the way that they work that I have not yet got my head around.

[asparkdeity]

e^i(theta) * f(z) rotates the image of f by an angle of theta radians anti-clockwise about the origin, and we restrict theta to some branch say [0, 2*pi). Which is why given some function f,

-f = e^(i*pi) * f

Corresponds to a 180 degree rotation of f about the origin, or rather as people more commonly know it, a reflection in the y-axis

[أبو.لحية]

Bro explained the foundation for why we need quaternions without mentioning it.

[nathanielmartins]

They are called imaginary numbers because no negative quantity that we have come across squares into a Negative, so we had to *imagine* a quantity that does.
But the more appropriate name for such numbers is Lateral numbers, because they represent an Axis lateral to the one we were introduced to in two Dimentional graphs.

[ChristopherGrey]

Thanks for doing math outside. I usually find it really distracting except for ratios and volumetric calculations, so the fact that you've popped up in my feed has been really inspiring.

[brianjohansson]

I am learning so much form you dude, keep it up ;D

[adil_]

Yeah, there so important that they appear in one of the most important quantum mechanics equation that is quite seriously fundamental for reality

[scptime]

think of it like this: whole numbers are for counting, fractions are for sharing parts, real numbers are to show a continuum, negative numbers show a debt or opposite, and imaginary and complex numbers encode 2d motion like rotation

[blazeegoingcrazy]

In fact, it’s not a circle, it’s a spiral, if we turn it, we could see the function of waves

[gallonsofwater]

Thank you for existing. You have satisfied my misunderstanding of the fundamentals of imaginary numbers. For real though, you make math fun.

[Marryatau]

This is the best way to explain imaginary numbers

[bluigimercury]

Then Schrodinger proceeded to tilt every Physicist in 1926 😂

[ItsPungpond]

The last sentence would most likely shock any math teacher

[bloxrocks]

I personally first got imaginary numbers when they came up in relation to springs