What's the physical meaning of imaginary numbers?

What are imaginary numbers? How are imaginary numbers used? Learn the physical reality and intuition behind imaginary numbers.

[Dzina-cs]

В видео о ковариантных векторах комментарии выключены, а у меня есть вопрос. Если можно, объясните, в объекте с переменной плотностью ковариантный базис используется и там, где плотность больше, и там, где меньше? Есть ли задачи, где одновременно используется и контравариантный базис, и ковариантный?

[angeldude]

The physical meaning of imaginary numbers is spinny. Quantum particles like to go spinny; kids like to go spinny and like toys that go spinny. Only no-fun adults don't like to go spinny so they call it "imaginary."

Forward: 1, 0°, no rotation
Left: i, 90°, counterclockwise (by convention
Backward: -1, 180°, reflection across the origin
Right: -i, 270°, clockwise (by convention)
Complete the circle by turning left one more time and you're back to 1, right where you started.

[spotify_ERROR]

thank you for imaginary perspective
is it possible to raise i or, e for example, to the power of a matrix

[sleepyelk]

nice explanation and poem at the end 👍🙂

[brendanhoxie]

Please help!!!

The cubic root of 1 is
-0.5 + 0.86602540378444 i

Time slows by 50% (-0.5) when traveling at 86.60254037% the speed of light!

It's also the cosine of 30

Does anyone want to tell me what's going on here?

[rer]

I thought you started off ok, but this is wrong and misleading so I had to reverse my initial optimism. You really started going wrong when you ignored the importance of the cycle of 1 to i to -1 to -i and back to 1. This is a quadrant cyclic concept not a wave concept and i is properly understood as an index of rotation into a quadrant associated with the previously mention cycle. Physically then - if you are traveling along the number line and you incorporate a change indirection (from positive to negative or the reverse) imaginary numbers allow you to count the angle of that turn. imaginary numbers are important in quantum mechanics not because both are wave functions, it is because imaginary numbers give a simple way to gage the spiraling behavior of waves - i.e. the rotation.

[ThinAirElon]

Nice video, By the way you are style is similar to WION palki sharma

[Мопс_]

It is surprisingly insufficient answer. From the video the first example is lame for me as
1. I haven't seen any calculations that would use such a weird way of counting.
2. It's locked on human interactions, it's not damn physics. Barely human logic that matches with how these numbers work.
So, I imagine that if quantum physics is one of the very few places where imaginary numbers have sense, it's safe to say they are useless to absolute most of people.