Imaginary Numbers Are Not Imaginary | Jeff O'Connell | TEDxOhloneCollege 

I was thinking the exact same thing...

Its not a math lecture to prove the application of complex numbers in mechanics, this topic is already known for centuries i gues. He just mention that imaginary numbers are not imaginary based on how we benefet from them in real life.

TedTalks...

You are completely right. He didnt make the connection between the imaginary numbers and the oscillatory motion he described at the beginning.

@Samson Jamari you dont have a girlfriend, incel

@Samson Jamari lol

@Samson Jamari das crazy yo but who asked

This video is meant to be an introduction to complex numbers not an extraordinary revelations. If you want to read something extradition then read a mathematic/ science journal

Thank you for explaining all of this! Very helpful!

that sucked

You have to learn about differential equations to understand why

Bold of you to assume enough people know about differential equations for that to be a reasonable statement

@@eyobwalid2332 I don't think Player was assuming that the audience knows differential equations. Just that in order to give a proper introduction to show why these examples have anything to do with sqrt(-1), would require an introduction to differential equations that would significantly make the lecture longer and probably lose half the audience.

If you are wondering the reason why his examples have anything to do with sqrt(-1), here's why. A differential equation that models vibrations, like the mass on a spring, is given by: m*y" + k*y = 0 where m is the mass, and k is the spring stiffness. y is the position of the spring at any point in time t. y" refers to 2nd derivative of y, which in this case is acceleration. One of the strategies for solving a DiffEQ in this form, is to assume y = e^(r*t), where e is a constant called Euler's number, and r is an unknown constant we'll solve for. Applying this to the DiffEQ, we end up with: (m*r^2 + k) * e^(r*t) = 0 e^(r*t) cannot be zero, so instead we solve the polynomial in front of it for r, to make that polynomial zero. Had the sign in front of k been negative, we'd have real solutions for r, equal to +/-sqrt(k/m). The solution then, would be a linear combination of exponential functions. However, the solutions are imaginary, and r = +/-sqrt(k/m)*i. Assign w to equal sqrt(k/m), to simplify our writing. This means the general solution is a linear combination of both of them. Assign arbitrary constants C1 & C2, to form this linear combination: y = C1*e^(i*w*t) + C2*e^(-i*w*t) Let C1 = (A + B*i)/2, and let C2 = (A - B*i)/2, where A and B are another two arbitrary constants. Our goal is to cancel the imaginary parts we'll eventually produce, so we can find a real world solution for y. y = (A + B*i)/2*e^(i*w*t) + (A - B*i)/2*e^(-i*w*t) Expand out e^(i*w*t) and e^(-i*w*t) with Euler's formula: e^(i*w*t) = cos(w*t) + i*sin(w*t) e^(-i*w*t) = cos(w*t) - i*sin(w*t) y = (A + B*i)/2*[cos(w*t) + i*sin(w*t)] + (A - B*i)/2*[cos(w*t) - i*sin(w*t)] After expanding it, you'll eventually cancel out all i's. The B/2*i*sin(w*t) terms add up, and so do the A/2*cos(2*t) terms. y = A*cos(w*t) + B*sin(w*t) And just as you expect, an oscillation is described by a linear combination of sine and cosine waves. No i's anywhere in this, which means this all happens in real numbers. But to show it from first principles, we had to appeal to imaginary numbers.

Real numbers are one dimensional. Imaginary numbers help make numbers 2 dimensional with special properties around multiplication for the imaginary number, namely i is a 90 degree rotation on a graph that repeats every 4 cycles under exponents. Multiplication of course doesn't work that way with real numbers. The names themselves are not important, it's just positive and negative numbers need to be in the same group of numbers since they share all the same properties and we have chosen to call that group, real numbers. Real numbers, negative numbers, imaginary numbers are technically "real" numbers if any number are real. Imaginary numbers were discovered when trying to solve cubic equations, which involved 3 dimensions and cubes, ie the real world we live in. Unlike quadratic equations where if they encountered square roots of negative numbers, they could decide there was no answer as visually on a graph it means the quadratic equation doesn't touch the x axis to have an real number answers, cubic equations have to cross the x axis at least at one point to give an answer because of their shape. There's some cubic equations with real numbers, that has an answer that's a real number. And for these specific equations, if you use the cubic formula, you must encounter the square roots of negative numbers. These eventually cancel out while doing the math to get the real number as an answer but you have to reckon with how to solve for the square roots of negative numbers to solve the formula. That's the original reason for the number i. With that you can solve for any answer in a cubic or any polynomial of n degrees, it will have n degree solutions. You can go back and solve for the answers of those quadratic equations that didn't seem to visually touch the x axis to have an answer. If they aren't found among the reals, they'll be found in the imaginary plane. All those imaginary answers perhaps don't exist in the real world, but the logic behind those imaginary answers stem from the original solution of specific real world cubic equations that had real numbers, that you had to pass thru the imaginary plane to arrive at the real number answer.

Best proof? What proof?

Professor​ @@user-ky5dy5hl4d

You have to learn about differential equations to understand how it relates to springs and pendulums

Yes you can

Haha - I guess I should check the comments more often. Sorry for the late reply! The answer is no! Imaginary and complex numbers will never be the answer to a real life application. They are a tool that allow us to solve real life applications. I hammer is a tool that, all by itself is not that impressive, but what you can do with a hammer...

@@Professor_O bro how is hammer comparable to the imaginary unit smh ur not teaching maths 😂

​@@Professor_Oimaginary numbers are essential for understanding circuits and current flow

I feel equally sad for your parents and anyone else who has to keep your company for extended periods.

Completely unrelated meaning of cis. Cis in this context, is a notation for cos(theta) + i*sine(theta). The c from cosine, the i from the imaginary unit, and the s from sine. Cis as in cismale and cisfemale, is the opposite of trans, and is a loanword from chemistry's use of the word. Look up cis and trans isomers, and it will make perfect sense to you, why cismale and cisfemale mean ordinary male and ordinary female.

Who is Alton brown ??

hahaha me too.

That’s what was going through my mind!

I did the best I could 😜

Imaginary numbers explaining the real World? Probably a joke.

@@user-ky5dy5hl4d I think real no. are symbols and along with axioms and operations, we use them solve real physical problems like geometric problems and things which we can touch and feel their existence. But at some point in history when mathemasians tried to solve problems like cubic equations, BTW in past mathematicians justify each step of solution by giving proof using geometrical shapes or other things which we can count or measure like when solving 2+x=6 mathimaticians solve it by imagining that there are 2kg and a weight of X kg on one side of beam balance and 6kg mass on otger side of beam balance so when we do 2+x-2 = 6-2 they justify this by saying that we are removibg 2kg weight on both side as the wieght on one side of balance left is x and other is 4 and it is balaced so it means that X wieghts 4kg so x=4 but at solving cubic equations they came across some steps in solution which have square root of -1, but there is no such thing in the world which can make sense i mean when i say square root of 4 it means 2 so mathematican immediately at that would place 2 apple or 2 meter length depending upon which physical thing they are using to justify each step, but when they started solving for cubic eq they find that square root of -1 occur in the middle step as an intermediate but at the end in the result such numbet cancel out and gave only answer in real no. Only. But they said how can we justify that step having square root of -1 because no such thing exist in nature so they said why not we form a number system which is multiple of square root of -1 though they don't have physical interpertation but they can be used in middle step of solving real world problem so these numbers were invented to help algebric calculations not to count physical thing but when complex plane was formed they thougt that, since square root of -1 make numbers on number line rotate so can be useful to take track of such system which in teal world rotate by asinghing one quatity to real axis and other to imaginary axis but remember imaginary numbers unlike real number are not invented to count physical things but they were invented for algebric world to solve its problems and the answer of real world problems but imaginary part at the end will cancel and answer will be in real numbers always! If real world answer is possible and if it don't come than it means it don't have real world solution!

​@@user-ky5dy5hl4dthey are essential for circuit analysis and current flow

Please share your immense intellect by enumerating your reasons the talk was terrible.