Are Imaginary Numbers Real?

The Imaginary number i was much debated long ago, yet is widely accepted now. But the question is: are imaginary numbers real? I mean, they're "imaginary" right? They don't actually exist....do they?

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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.

#math #brithemathguy #imaginarynumbers

[anjamoro]

square space? Nah, I'll stick with complex space

[EduIreland]

Great video, only thing is that "complex" doesn't mean complicated.
Complex: having multiple parts or aspects that are usually interrelated
Complicated: involving a lot of different parts, in a way that is difficult to understand

[Dark_Slayer]

How to win internet arguments:
1:42
that's BORING + what if you're wrong?

[rextanglr]

short answer: it depends on what your definitions of "real" and "imaginary" are.

[flowingafterglow]

I remember as a yoot always being confused when the teacher would clarify that this only applied to "real" numbers. I couldn't understand what a "non-real" number was. Learned i in algebra 2 in high school, and complex analysis was one of my favorite classes in college. Complex analysis is still one of my favorite topics.

When I talk to my kids about it nowadays, I tend to go back to that number line representation, and ask, what happens if you step above or below it? They might object, but I will remind them what when they started, they only had the positive values, so they learned to step to the left of 0. Now think about stepping above or below.

I think conceptually it helps them to grasp the idea, although still not the significance, and definitely not the features.

[ivoregueroferrer]

They told them imaginary because of their way of solving the equations, they drawed literal squares to do the equations and it was illogic to think of something with negative area.

[Diaming]

Quantum mechanics uses complex numbers to describe quantum phenomena, not just to calulate things in between.

And yes, you can't make math grounded to reality. There is nothing wrong with coming up with anything as long as it's logically consistent with the rest.

[DavidRomigJr]

Imaginary numbers are more intangible than imaginary. Can “i” stand for that?

And I recall working with Quaternions and having i, j, and k along with a “real” part, because sometimes traditional complex numbers aren’t complex enough. Though it did teach me t think of imaginary numbers as a perpendicular phase shift— which makes it easier to imagine in my head.

[richardtrager]

Complex numbers are also used in ac circuit analysis like adding up two sinusoidal signal with phasor.

[jakubpacua]

In Poland we have even worse. Imaginery numbers are in polish called, ,urojone" witch means like something imagined by somebody with mental illness. And for complex we have, ,zespolone" (compound) witch is correct name i guess but it sounds a little akward to me

[hric.martin]

I really wish Bri would go on to the topics of quarternions and what other more complicated number systems are possible or impossible and why

[orisphera]

1:40 There is another problem with not having no square roots of negative numbers: the cubic formula requires them when there are 3 solutions. It's possible to solve cubic equations without using complex numbers explicitly, but in this case you have to consider that a separate case

[EastBurningRed]

The better question is "are real numbers real?"

[wallstreetoneil]

In the history of numbers, humans took longer to accept negative numbers (thousands of yrs), which are just an equal distance from Zero in Opposite World, or better yet, a 180-degree rotation around Zero, than it did for Mathematicians to accept 90-degree rotations (a halfway stop along the way to Opposite World) - which we now called (i). Once you accept negative 4 bananas, 4 imaginary bananas (a quarter rotation away from 4 'real' bananas), isn't as big a jump. Humans innately understand rotating - it's the math of rotations

[jasonreed]

Anyone who dislikes imaginary numbers doesn't know the glory of the Laplace Transform and frequency domain solving all your problems. Laplace is the easiest way to solve differential equations and Euler's equations are the basis for making calcutions for anything involving AC electricity not trigonometry hell. (When 120cos(2π60t + Φ) becomes 1<Φ life becomes so much easier when you need to multiply that by another sinusoide to find power.

Don't become an EE if you don't like complex numbers, they are everywhere and make your life easier.

[Phi]

The issue isn't that imaginary numbers aren't real. The issue is that negative numbers are not real. We say they're real, but we have made up negative numbers because they're useful when talking about _taking away_ number (i.e. subtracting). But subtraction can really be thought of as addition in reverse. For instance, when we take away three oranges from a number of oranges, we think of it as subtracting three from a number, but we can also think if it as _adding_ three oranges to the universe of things that _aren't_ the remaining number of oranges. It's this dual, mutually dependent and proportional nature of addition and subtraction that creates the bizarre property of negative numbers, and, thus, imaginary numbers.

[thalt]

"What exactly is imaginary about a number like i, and what exactly is real about a number like pi"
That was literally so clean

[Helmutandmoshe]

As the great mathematician Paul Bernays wrote about the objective reality of mathematics described by Plato and their analogs in today's mathematical world - "This application is so widespread that it is not an exaggeration to say that Platonism reigns today in mathematics."

[meqdadv]

the best way that helped me in understanding complex numbers is seeing them as motions
because every complex number can be associated with a vector and a vector represents moving a point in the direction of the vector and with speed equal to its magnitude.
but now I have no idea what numbers actually are !!!

[fariesz]

speaking of math teachers: my teacher in year 8 went on a rant once about how it were utterly incorrect to put arrow heads on both ends of a number line. i see there is no agreement on this subject in academic circles