why would you use euler's formula for phase shift if you can use sum to product formula?

Please answer this- I'm an undergraduate. Going to university next year actually. I was just wondering after getting Bachelor's in EE can u study Master's and do a part time or full time job at the same time. ??????

@ Fugitive Yes however your master's may take more time since you may not be taking the full load of classes a "normal" full time grad student would (instead of finishing in 2 years maybe 3). It also depends on you and how well you could time manage and balance responsibilities.

MajorPrep I mean the software draw the math function pro😂

@Figitive Part time working, yes. But full time working, your master will probably take a very long time!

Quahntasy - Animating Universe Always preferred saying complex numbers instead

Complex numbers have a real and imaginary part, with i being the imaginary part.

@@azizalaliq8 Actually i doesn't belong to the imaginary part. The imaginary part is what you multiply i with.

Lateral Numbers

And second wa you were born

xD

Hello tibbee. You watch his videos too!

Thank you Toby! I've been a fan of your channel since I came across your 'astrophysics exam unboxing' video a few months back. Would be interesting to see this topic from a physics perspective though. Keep up the good work!

@@zachstar toby

LOVE YOU TIBEES! DAY 1 SUBSCRIBER!!!!!!

yes offcourse.....all those artists and people that you love but never met them before and all that money that you dont have...you cant count them and you will get an IMAGINARY RESULT ))))))

my friend count : 10i money : $1 M . i

No, because “imaginary numbers” really exist, unlike your money and friends

@@AndresFirte True. LOL

you cannot use negative numbers to count your friends either ;)

Math is logic disipline that’s taught as a series of memorization course in grade school. In reality you could teach a kindergartener Calculus given that you explain the logic carefully enough

that’s how the education system (at least in America and I’m pretty sure most of the world) works. Most students don’t really care about anything learnt in classes that involves calculus, take it from a current sophomore in high school. So students learn it to memorize since it’s easier than to fully understand it and its applications

It doesn't help that when a concept is first introduced the teachers explain it using formal math lingo which there is no way the students will understand, at least not at first. So basically the least resistance path to getting a good grade is to memorize a bunch of equations, and learn the mechanics of the exercises by doing a lot of them. This way a student can get a very high grade without ever having a proper understanding of the concepts behind what they are learning. Of all disciplines taught at school I think Math is the most broken out of them all imo in how poorly it's being taught

@@miguelpereira9859 facts

@@miguelpereira9859 I'm glad to see this mentioned. Most people learn by rote memorization, because it's made needlessly complicated by things like asinine vocabulary, and in truth most people don't have a concrete way to make it applicable to their daily lives, and they never will. Mathematics as taught isn't "just logic bro" as some claim, it's a game of trying to decipher the hidden message of the esoteric math cult. It's hard to answer something when the question itself needs to be explained. The established syntax is why a lot of people struggle with math, and that's the facts. Sadly if anything were ever formally done about it, I'm sure things would end up significantly worse, if other school initiatives are anything to go by. I think it's something teachers should just keep in mind.

I haven't seen that before Just kidding I'm a Mathematician ,well at least I will be.

Just Why? And why did 214 people agree w u wtf

he should have done "this is a graph of sinx, if you haven't seen this before you should probably click away now" 😂

Yess, pls more!

Actually, math and science have only made me more depressed. Sure I see more connections, but I also have a lot more questions.

@@thewalkingjoke3843 so... You haven't started understanding it?

@@James-jh3sz Thing is you can't understand these things right away. I studied complex numbers and Advanced calculas in high school. I am in 3rd year of my college degree and now I understand almost everything.

@@alokbaluni8760 I agree, but the person i responded to seems to be the type of person to overestimate themselves which is why I was saying that.

@@alokbaluni8760 You can’t understand Advanced Calculus without first understanding all of Elementary Calculus and Linear Algebra.

@@randylejeune Complex*

Andy Dufresne well in my country there is 2 type of maths. Emath and amath. E math is elementary math (applicable to the real world) and additional maths.

I feel like explaining math would have the reverse affect for a lot of people. So many are simple minded and if explanations dont come naturally they give things a bad stigma and choose to neglect the importance of things. For people like myself and some of the others in the comment section im sure what you said makes sense. When I am perplexed by an idea I stop at nothing to fulfill my need to understand things. I personally was a little frustrated in school because like you i got to points in school where i had eurika moments in regards to specific concepts that I feel i couldve been explained in middle or high school and still understood. So the part thats like you i had wished they had just explained things in ways earlier on to build understanding. But instead the school systems focus on solely applications of math so people can just simply understand how to evaluate problems and feel good about getting to a definite answer. With or without an in depth explanation. Some would rather not have that in depth explanation because they will realize the extremes of what they are getting into and stop.

@@woooshwooosh2867 from SG

People who don't *want* to understand mathematics will never understand mathematics. The trouble is, we've made it socially acceptable to be *proud* of not understanding, and not wanting to understand, mathematics.

@Yani Zhou Because ypu're spending thousands of dollars for this exact reason? And because children mostly don't care that much about school.

SMH. could’ve said “hold my roots”

@@shayorshayorshayor *hold my root beer

Engineering students don't even know what "being happy" means

@@jimmyh2137 why is that?

@@jimmyh2137 haha you said big funni stereotype I must like now

@@wetfart420 I know how to find more digits of pi. That is, I theoretically know any finite number of digits of pi (given enough time)

@@wetfart420 I know all numbers of pi

I know the last 2 digits of pi

I know all of Pi in a base-Pi number system

@@jordanwoods728 that's smart

hello vector

Just finished calc. This hurts so much.

Radians are fucking annoying, I'm much more used to more basic units.

Sees someone spell a word incorrectly TRIGGERED

Triggered by what? Degrees are equally, if not more, helpful and convenient to use compared to radians.

It doesn't matter. When I use reading word synthesis, I use degrees because I cut 2pi out of my mind. That way I make less error. When I am analysing the stability,observability,Linearity, Controllability and a lot of other things I prefer to go in rad/sec. They make the math in both of these cases simpler.

Degrees have much more real world application than radians. Radians are only correct on the unit circle technically. Unless you always make whatever radius you have one unit but personally if my circle has a radius of 3.5m then that's not one unit.

Thanks✌

Actually he is right. No measurement gives you an imaginary number. We are talking about measurements in an experiment. A quantity can be complex but you can measure the magnitude or real part only.

You can't measure an imaginary quantity in quantum physics otherwise it wouldn't be Hermitian

@@epsi what...

well just a heads up AS level physics is boring and AS maths is easy af dk about Further maths

Because the average person doesn't care about 'i'

People are scared of mathematics.

Because it's terribly explained. A maths student and an aspiring tutor opinion. Sorry... Too less explanation, presenting new ideas as if I'm supposed to be familiar with them in order to follow along, but also be surprised when seeing they make use of i. My moral of the video is "i is useful in maths describing how the universe works, although I have no idea how really"

Becous it only shows the real part.

@@nitsanbh but you will know if you study it?

Kalumba mutembo agree

Agreeeeeed

No, I'm in second year (bachelor degree) and i don't know it yet

Do you study maths?

Carlos Dominguez Nope, just the joys of KZfaq recommendations algorithm.

Why are you replying to a year old comment?

@@livethefuture2492 I don't know, just I did it

@@livethefuture2492 Two years later (and a year from your reply) and I understand the concepts in this video - still nothing of how it’s used. Quite interesting that I got this recommended to me yet again, I completely forgot about this comment.

There's two possible reasons why your teacher gave that response: 1. Your teacher never learned the applications of complex numbers 2. The background knowledge you'd need to know to understand their applications, is far beyond the scope of the class. For instance, you'd need to know the background of electric circuits, and what capacitors and inductors even are, to show you how to apply complex numbers in this particular real world application.

It’s explained using Elementary Calculus.

number e complexia

hows it going

A pure math major friend of mine back in the day described i as just the thing you basically put in an equation that makes an orthogonal rotation away from the equation that still relates to it, relate to it. So every time you add i in the circuit diagram I just see it as an extra dimension of relation that affects it but doesn't actually change the literal position directly. Does that even make sense?! Like.... adding an extra orthogonal vector arrow at all points that can be manipulated?

I've loved imaginary numbers since I was told about them by my dad when I was 6, maybe 5.

Resistance refers only to the opposition of a component to conduce electric current, impedance refers to the factor that relates a voltage with it's current or vice-verse (Basically Ohm law but instead of the R, it's a Z which stands for impedance). Resistance is actually an impedance, but just for the case of a resistor, as capacitors and coils have a different expression for their impedance that relates to it's capacitance and inductance respectively.

@Justin Chan The impedance of a circuit has two components; 1) Resistance : how the circuit resist the current by heating up 2) Reactance : how your circuit augment or diminish vibration of current Those two together will determine how your AC circuit reacts. For exemple, an Electric motor in a circuit will make your circuit vibrate, which will result in less usable power in your circuit. In order to reduce reactance, you will add an capacitor to your circuit to tamper vibration.

(i^4)st

No pi-th

So, you didn't watch the video, but only imagined it?

Flick Penrose yup

Totally right, my mistake

How did you determine that?

Owen you just compute cos(15)+cos(50) in degrees

Or add .966 to .643 like a normal person

Yes

Yes. I got the same answer as you got too!

Actually, at 8:11 he made a mistake. 0.966 + 0.643 = 1.609, so the next slide should have said 1.609 + 1.025i. But then 1.908e^(32.5 deg)i is correct.

He is just basically showing you that imaginary numbers is a very useful tool to deal with complicated physics equations. Thanks to euler's identity, we can use imaginary numbers to manipulate real functions (physics laws), i.e. treat them as the real part of complex functions (imaginary numbers as inputs and outputs) because lots of useful calculations are easier in complex domain. This series in the following link is much much better than this video, though it doesn't go into engineering applications of them. kzfaq.info/get/bejne/ipxkaqZ42Nuzhok.html For better explanation of Fourier Transform, which is a big deal in electrical engineering, see this: kzfaq.info/get/bejne/qdaFgdOqq5ucco0.html

Sonay Yalım Sonay Yalım i was watching dash cam australian when youtube recommended me a video about imaginary number[the first video link, ”imaginary numbers are real”]!!! so, awesome. the i stumbled on to this: kzfaq.info/get/bejne/f7uEeqmC1bHFgIk.html

cries every time i is used instead of j

Found the engineer

@@Mot-dh5sx Cries every time i or j is used instead of k. quaternions and their imaginary, joke and kooky numbers

Multiplying by i rotates a vector (or a phasor as I really learned it) 90 degrees in the complex plane actually. From what I talked about in the video you can use eulers formula to see that i is the same as e^90i. so multiplying by some other exponential will result in addition of exponents and by adding 90 to the angle but keeping the magnitude the same you end up with the same vector rotated 90 degrees.

Multiplying any constant with i just tells that that quantity is just lies in the imaginary axis of the 3d complex graph. Moreover real things which has tendency to holds it's shape and size, under all circumstances, doesn't come near to i. Complex numbers definitely helps us to make the math of something changing or the math of changed quantity w.r.t. some other Changing quantity easier for us to understand.

I would like to see that prove

Emil Müller :v well I can email it to you if you like. You can get in touch also in Skype , my ID is " haniffdin " . You can get my smartphone number from there also and use other chat apps, sms or iMessage etc.....

lol, good one

@@hanniffydinn6019 You lost such a good opportunity to say "I'd send you the proof, but the margins of this comment section are too small" Such a waste of potential...

Naimad Granted, bit of cliche though I thought. Nobody has enough brain cells to even ask, never mind the joke !