Imaginary Numbers are NOT what You Think They are!

[@BrainStationAdvanced]

5:48 Let me know if you want me to make a video on Eulers formula and its real life application

[@bossofdarkness0528]

Yes! I've been confused about Euler's number, and we need you to teach us.

[@adameve8600]

Yes

[@hamzaHamza-km2ng]

abseloutley

[@storieswithfarouk6739]

Yes

[@BooklishH]

Bro, Your videos are amazing!! I Don't know how this is not reaching peak, making everyone understand such topics so easily, you deserve my praise

[@BrainStationAdvanced]

🙏

[@pecugihan]

remember the way to write vector (like 2i+3j), it similar to complex number too, but in complex number (like 2+3i) it just dot, I think complex number is like writing dot in vector way

[@user-wl4zu2ok1e]

The coordinates of the third vertex can be determined as follows: 1. We start with an angle of θ = 120 degrees. 2. The point can be expressed as (-1 + isqrt(3)) * e^(i120). 3. Using the formula e^(ix) = cos(x) + isin(x), we can rewrite this as (-1 + isqrt(3)) * (cos(120) + i*sin(120)). 4. This expression simplifies to -1 - i*sqrt(3). 5. Therefore, the coordinates of the third vertex are (-1, -sqrt(3)). As an addition, the area of this triangle can be determined as follows: 1. Using the determinant formula for the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3): Area = 1/2 * |x1*(y2 - y3) + x2*(y3 - y1) + x3*(y1 - y2)|. Substituting the coordinates (2, 0), (-1, sqrt(3)), and (-1, -sqrt(3)), we get: Area = 1/2 * |2*(sqrt(3) - (-sqrt(3))) + (-1)(-sqrt(3) - 0) + (-1)(0 - sqrt(3))|. 2. Simplify each term: 2*(sqrt(3) - (-sqrt(3))) = 2*(sqrt(3) + sqrt(3)) = 4sqrt(3). (-1)(-sqrt(3) - 0) = sqrt(3). (-1)*(0 - sqrt(3)) = sqrt(3). 3. Add these results: Area = 1/2 * |4sqrt(3) + sqrt(3) + sqrt(3)| = 1/2 * |6sqrt(3)|. 4. Simplify further: Area = 3*sqrt(3). Thus, the area of the triangle is 3*sqrt(3) units squared.

[@ElectricGamer_YT]

4:07 - just wanted to point out a little nitpicky thing. It's the imaginary number line. Both axes together make the complex plane, but the imaginary axis by itself is just imaginary. (It is also technically complex because imaginary numbers can be written as 0a+bi, but we usually don' call it that.) Great video though!

[@BrainStationAdvanced]

Right 👍

[@prithvisinghpanwar007]

my brains still not braining

[@heenakhandelwal8608]

This is a banger! I have never heard such an explanation for imaginary numbers. Thanks :)

[@ZDTF]

0:51 and that two😂😂😂😂😂 hahaha

[@WilliamWizer]

unless I'm talking to people that don't know sh*t about "imaginary numbers" I prefer to call them "lateral numbers" we can move forward (positive numbers), backward (negative numbers) or lateral (at a 90º angle. the, so called, imaginary numbers) it's the same thing we find when the irrational numbers were discovered. they were given a very horrible and cruel name. they have nothing irrational on them. even "negative numbers" feels wrong and cruel. people at those times didn't knew how to name things.

[@NevadaMostWanted658]

Finally, numbers i can count my money with.

[@ky7299]

i = (0, 1). x + yi = (x, y) = (x, 0) + (0, y). C is R^2 equipped with a product operation that makes it a field. I've always found the notation "x + yi" quirky and misleading although it works.

[@alithedazzling]

nice video ;)

[@BrainStationAdvanced]

Thanks!

[@wildbill7267]

My bank account balance is imaginary 😂

[@CalculusIsFun1]

That third one would be (-1,-root(3)) right?

[@vashahri]

Good luck. You'll be monetized by less than a month. Did you use AI for narration?

[@Rg-nk3rc]

i is always forgotten just like me

[@BrainStationAdvanced]

🥲

[@KSd-z3m]

Pls explained polynomial graph ❤❤❤

[@BrainStationAdvanced]

What is a polynomial graph?? Can you pls elaborate? is it like "how to plot polynomials on a graph" kind of thing?

[@sujanrajakannan]

Other vertex is (-1,-√3)

[@frodotingaming5528]

I want tricky questions based on physics

[@sujanrajakannan]

i=√-1 e^iθ=cosθ+isinθ θ=90° e^i90°=cos90°+isin90° e^i90°=0+i1 There fore ×i is the effect rotationing things 90°

[@grantorino2325]

The remaining vertex is (-1, -√3).

[@ZDTF]

0:46 They all 2? Cuz equaitralntreiangle

[@Blocky_Skillz909]

1:38 People don’t care about you anymore? I’m pretty sure you got a lot of fans who cares about you

[@BrainStationAdvanced]

😂 I see what you did there

[@KSd-z3m]

❤❤❤❤❤

[@christopherrice891]

Okay so i have a question. Imaginary numbers mean an angle of rotation, right? What do the imaginary numbers mean then in quadratic equation roots or systems of equations roots? Can imaginary numbers like those be angles of rotations too? May i please have somebody tell me? I would really appreciate it!

[@user-wl4zu2ok1e]

Imaginary numbers do relate to angles of rotation in the complex plane. In quadratic equations, when you get imaginary roots, they usually show up as points that are a certain distance from the origin on the imaginary axis. These numbers can definitely be thought of as rotations, particularly when you’re looking at them in terms of complex numbers and their polar form. For example, in the equation (x^2 + 1 = 0), the roots are (x = ±i), which can be seen as 90° rotation from the positive real axis in the complex plane. If I didn't answer the question you intended, could you elaborate on it more specifically?

[@christopherrice891]

@user-wl4zu2ok1e Suppose we have the complex roots 2+3i and 2-3i from a quadratic equation, please explain these roots in rotations terms. Or 1-2i and 1+2i, or 4+2i and 4-2i. Those are my questions elaborated more specifically.

[@kazedcat]

​@@christopherrice891Complex quadratic roots are the points that cross the x axis on a third dimension. So you have a quadratic curve drawn in an xy plane this curve becomes a 3d surface when the domain is extended into the complex set.

[@christopherrice891]

@@kazedcat Please tell me more!! You got my undevided attention.

[@user-wl4zu2ok1e]

@@christopherrice891 To find the angle of a complex number, you use the arctangent formula: theta = tan^(-1)(imaginary part / real part). For example, for 2+3i, the angle is tan^(-1)(3 / 2) which is approximately 56.31 degrees, while for 2-3i, it’s tan^(-1)(-3 / 2) which is approximately -56.31 degrees. Similarly, for 1+2i, the angle is tan^(-1)(2 / 1) which is approximately 63.43 degrees, and for 4+2i, it’s tan^(-1)(2 / 4) which equals 26.57 degrees. This method gives the angle each complex number makes with the positive real axis.

[@Aladin-tp1]

So if sqrt(-1) = i so waht is sqrt(i) ? 😅

[@vinijoncrafts2882]

kzbin.info/www/bejne/kGWcmYulg5l-jcksi=iuptBsg9SUAWcVEv

[@angelommv]

45°

[@user-wl4zu2ok1e]

45° and 225°

[@wernerviehhauser94]

All numbers are imaginary...

[@Thrillzrobloxbedwars]

No that is not true as all numbers are a representation of logical facts as math is logic. That is also like saying words are imaginary because we invented them as humans but this is not how it works as they represent facts.

[@storieswithfarouk6739]

If you mean that all numbers are complex then that's technically true because 5 for example is really just 5 + 0I, which is complex, but saying all numbers are imaginary is wrong because 5 or real and so are all other real numbers. numbers

[@wernerviehhauser94]

@@storieswithfarouk6739 I am very well aware of the difference between the real numbers, imaginary numbers and complex numbers. What you don't get is the fact that there is no "5" in this universe. 5 apples, 5 stones - yes. But the concept of "5" is a creation of the human mind, therefore "made up" or imaginary.

[@Thrillzrobloxbedwars]

@@wernerviehhauser94 Not everything that is a concept made up by humans to understand the reality is imaginary. It's because the concept describes something that is real so if you consider it imaginary how come it describes something real?

[@Hello1-t1y]

😂

[@hamzaHamza-km2ng]

(-1;3i)

[@ZDTF]

Call my girlfriend I Because shes imaginary

[@Karthik-ut3vo]

😅

[@Karthik-ut3vo]

Better you turn 90° let see you get a girl friend... real life application 😂😂😂