Same here, I know a little bit of French so I knew my teachers weren't pronouncing it right, I just needed to be sure, and this teacher did not disappoint
Can I apply De Moivre's theorem on all examples below to convert polar form to rectangular form? ex 1: √2(cos(45°) + 𝑖 sin(45°))² ex 2: √2(cos(45°) - 𝑖 sin(45°))² ex 3: √2(- cos(45°) - 𝑖 sin(45°))² ex 4: √2(- cos(45°) + 𝑖 sin(45°))²
@Learn How not when Eddie Woo is teaching. Flip my lecturers made this stuff seem bloody impossible making things needlessly complicated with weird notation. Its how its taught that makes it easier.
Given: (216/343 * i)^(2/3) Rewrite the exponent as two exponents, such that it is a squaring and a cube root: ((216/343 * i)^2)^(1/3) Carry out the squaring of the base: (216/343 * i)^2 = -46656/117649 Take the cube root of the magnitude, to find the radius of the circle, on which the three cube roots will reside: cbrt(46656/117649) = 36/49 Because we are taking the cube root of a negative real number, the real-valued root will be negative and real. Odd roots in general, of a negative real number, will be negative real numbers, since (-1)^odd = -1. This means the first root we find, will be -36/49. Per DeMoivre's theorem, the remaining two roots will be uniformly distributed around the complex plane. This means one of them will have an Argand of pi/3, and the other one will have an Argand of -pi/3, while the principal root has an Argand of pi, as a negative real number. Thus our answers are: z1 = -36/49 z2 = 36/49*e^(+i*pi/3) = 0.367 + 0.636*i z3 = 36/49*e^(-i*pi/3) = 0.367 - 0.636*i
Simple application of the laws of exponents, for a power raised to a power, with the base and first exponent grouped. In general, (x^a)^b = x^(a*b). So for e^(i*θ) raised to the n, it becomes e^(i*θ*n). e^(i*θ) is commonly noted as cis(i*θ), which therefore means that cis(θ)^n = cis(n*θ).
An example I can give you, is the application in electrical engineering. Capacitors, inductors, and resistors, can all be generalized with the concept of impedance. So that rather than thinking about a special formula for each of these circuit elements that relates voltage and current, you simply extend Ohm's law for resistance, to a complex version of Ohm's law with impedance. An AC (alternating current) waveform can be represented as a complex number, where the magnitude is the amplitude of the waveform, and the Argand is the phase angle. Think of the complex number rotating on the complex plane, and projecting itself onto the real number axis. The projection on the real axis tells you the waveform's value in real time, while the imaginary parts tell you a forecast of the past and future of the waveform. Voltage and current are each waveforms like this, where they are given in the form of V(t) = A*cos(w*t + phi), where A is the amplitude, w is a term related to the frequency, and phi is the phase shift, from the original cosine function defined as a phase of zero. You can represent this waveform as a complex number, in the form of V = A*e^(i*phi), which in Cartesian form is A*cos(phi) + j*A*sin(phi). Note: EE's use j for the imaginary unit, because the letter i is spoken-for to stand for current.
Onto the example: A 60 Hz waveform of 100V amplitude is applied to a 100-Ohm resistor and a 100 millihenry inductor in series. Find the amplitude of current, and the phase shift from the source's voltage waveform. Resistor impedance: Zr = R Inductor impedance: ZL = j*w*L Value of w, for 60 Hz = 2*pi*60 = 377 rad/sec Thus: Zr = 100 Ohms; ZL = 37.7 j-Ohms Find the net impedance of the circuit: Znet = Zr + ZL Znet = (100 + 37.7*j) Ohms Let V have a phase angle of zero, to keep it simple. Use V = I*Z, and solve for I, to find current. I = V/Z I = 100V / ((100 + 37.7*j) Ohms) Carry out the complex number math, and get: I = (0.876 + 0.330*j) Amps or in Mod-Arg form: I = 0.936*e^(-j*0.36) Amps Amplitude of I = 936 milliamps Phase angle of I = -0.36 radians, or -20.7 degrees The negative indicates that current is delayed from voltage, as is expected for an inductor.
@@carultch thank you so, so much for breaking down this example for me. I am not a “math person” as you can see, but I am infinitely curious about the world and often wonder how this kind of maths is applied in our world. You are greatly appreciated. ❤️❤️❤️
@@rakeshbai2732 No problem. Glad I cold enlighten you. I'd like to have seen more applications of complex numbers when being introduced to them in my math class. Unfortunately, a lot of them require background knowledge that is far beyond the scope of what you are expected to know as a high school student. The most electrical background you can expect students to know at that point, is maybe the basic relationship among current/voltage/resistance and the two Kirchhoff rules. But who would know what a capacitor or an inductor is? Or the AC specifics?
His energy is so high. I want to join in his class !
What I would do to have a maths teacher as passionate as this guy
There is no way that this is gerard from my class in CTC. How have we both ended up here hahahah
The pronunciation of Moivre is more hard than the formula
harder*
@@katarixy *harderer
@@peeper2070 hardererer*
@@nayankumarbarwa4317 *herderererer
facts
Finally found a teacher who really want to teach.
I only watched it to know how to pronounce Demoivre.
Haha same. He says it at 3:42 for anyone else, with the pronunciation explanation from 2:50
Me too
@@jennylf1 thank you, this was helpful lol
Same here😂
Same lol
watching this as a physics undergrad student in UK and found it very useful! Cheers
Watching this as an engineering undergrad. This guy seems like a good teacher
Same. Which uni?
Do you recommend physics as a student yourself? I'm taking international a level physics
yes@@longstoryshortisurvived
what a lively class dynamic!! your class seems like fun
nah
@@verypython3667 not for ppl living on last braincell
@@kingpatil2882 "living on last braincell" haha classic
I wish I was in his class. His energy, his way of teaching makes you want to learn.
I would actually ENJOY math classes more if they had this sense of humor and simple explanations...
For some reason, this guy reminds me of Tintin.
Who wouldn't want to be in that class!
Teachers ought to be like you- explaining things in a jovial manner
The expression on my face is like Ant-Man's when he's watching Thor explain the infinity stones 😁
thank you for this
1:36 this is actually the correct pronunciation of "theta", in greek.
Thanks for sharing that
Reminds me of people pronouncing Euler as 'wheeler'.
First math teacher who is teaching the pronunciation
I like how confident he is
This is the 3rd video in the series - Multiplying Complex Numbers. Will help to see those videos.
I'm gonna say Moy-vray out of spite now
After that, it's disturbing to explain how to prononciate "De Broglie"
borispider it is pronounced as de broy
@@piyushdaigavhane3488 Jean-Michel Premier-Degré !
😂 I called it 'debrog-lee' for 2 years. Only found out last week it's de broy
You are good teacher
Love you from India 🇮🇳🇮🇳🇮🇳
जय श्री राम 🚩🚩🚩🚩🚩🚩🚩
Maths at uni student checking in for awesome videos, thanks
WOW This was a lovellyy lecture
I only came here to find out how to pronounce De Moivre, and I'm leaving satisfied
Same here, I know a little bit of French so I knew my teachers weren't pronouncing it right, I just needed to be sure, and this teacher did not disappoint
The Teachers Vibes change everything
i love this class!
Truly amazing, keep it up
I loved your explanation.
so lovely.....I also want to join you Class soon
Can I apply De Moivre's theorem on all examples below to convert polar form to rectangular form?
ex 1: √2(cos(45°) + 𝑖 sin(45°))²
ex 2: √2(cos(45°) - 𝑖 sin(45°))²
ex 3: √2(- cos(45°) - 𝑖 sin(45°))²
ex 4: √2(- cos(45°) + 𝑖 sin(45°))²
ye
no first convert these in the form of r(cos(theta)+ i sin(theta)) form using trignometric conversions on theta
I am looking for a video how to pronounce De moivre thm. And i found the right one😌
This man is my saviour
in india, we call it the maurya theorem. FOR REAL (maurya is also the name of our maths teacher so..)
DMT... Joe Rogan approves.
I was about to comment this
He explained pronounciation of demovire half the time 😅
I was actually expecting the theorem for rational index
Love from India
I can say De Moivre. Time to book my plane tickets to Paris. I'm practically a local
the pronunciation is this: *Demuavg*
thanks so clear and fun too!
Nice video, I now understand
love it.
this made his bodycount quadruple fr on god
thank you
what a teacher ❤️❤️😂
my teacher just shows us links to this guy instead of teaching us herself
If anyone can answer me can u tell me where i take this ? College or school?
تاخذة بالسادس اعدادي بشكل مبسط وبالكلية تاخذة موسع
@@ahmedsteve9205 برو اني طالب سادس اريد اشوف وين يدرسونه غير العراق
legend
I think Argand is Swiss Mathematician
Yup, I probably mispronounced that in my first video. Good thing I only mentioned it once.
This stuff is 1st year engineering degree mathematics. Do these high school students actually understand this stuff?
@Learn How not when Eddie Woo is teaching. Flip my lecturers made this stuff seem bloody impossible making things needlessly complicated with weird notation. Its how its taught that makes it easier.
Maybe in your country, or the country where you are studying. In the UK this is A level standard.. it's covered in the double maths A level.
in the UAE this the eleventh grade curriculum
Yes it's covered in grade 12/13 (year 12/13) Further Maths in the UK. Majority of the population only takes Maths and not Further Maths.
Yeah this is the extension 2 course which covers the basics in University material. From NSW
That right there, was inspired math
2:42 for everyone who came to learn how to say De Moivre
3:44 pronunciation of “de moivre”
:) thank you.
in one word thanks
2:21
why the students shout the hell out !
I read "mate" as "muyte"
Great instructor but the students seem rude and are constantly chatting. I feel sorry for Mr. Woo :-(
Hand out a few detentions to get them back in line.
The students should shut up bruh
my teacher calls it de moy-vreys theoram 😭😭😭😭😭😭😭😭
Hi
I have a question
Use de moiver (216/343i)raised to the exponent2/3
يمكن ذلك باستخدام نتيجة مبرهنة ديموفر
Given:
(216/343 * i)^(2/3)
Rewrite the exponent as two exponents, such that it is a squaring and a cube root:
((216/343 * i)^2)^(1/3)
Carry out the squaring of the base:
(216/343 * i)^2 = -46656/117649
Take the cube root of the magnitude, to find the radius of the circle, on which the three cube roots will reside:
cbrt(46656/117649) = 36/49
Because we are taking the cube root of a negative real number, the real-valued root will be negative and real. Odd roots in general, of a negative real number, will be negative real numbers, since (-1)^odd = -1. This means the first root we find, will be -36/49.
Per DeMoivre's theorem, the remaining two roots will be uniformly distributed around the complex plane. This means one of them will have an Argand of pi/3, and the other one will have an Argand of -pi/3, while the principal root has an Argand of pi, as a negative real number. Thus our answers are:
z1 = -36/49
z2 = 36/49*e^(+i*pi/3) = 0.367 + 0.636*i
z3 = 36/49*e^(-i*pi/3) = 0.367 - 0.636*i
I'm french and your "r" pronunciation at 3:33 is completely wrong ^^ But nice try I admit it's not easy. Also thanks for this video
I don't know what that guy's problem was but you were obviously just trying to help.
@@pigeonlove i also want some of that cocaine
استمر ستاذ بس سؤال ما فهمته
math video spends 2:30 to 3:50 on english
I don't understand why when you put cis(θ)^n, it becomes cis(nθ). can someone pls explain?
Simple application of the laws of exponents, for a power raised to a power, with the base and first exponent grouped.
In general, (x^a)^b = x^(a*b).
So for e^(i*θ) raised to the n, it becomes e^(i*θ*n). e^(i*θ) is commonly noted as cis(i*θ), which therefore means that cis(θ)^n = cis(n*θ).
Can anyone tell me why this is important in and how they are applying it I their studies?
An example I can give you, is the application in electrical engineering. Capacitors, inductors, and resistors, can all be generalized with the concept of impedance. So that rather than thinking about a special formula for each of these circuit elements that relates voltage and current, you simply extend Ohm's law for resistance, to a complex version of Ohm's law with impedance.
An AC (alternating current) waveform can be represented as a complex number, where the magnitude is the amplitude of the waveform, and the Argand is the phase angle. Think of the complex number rotating on the complex plane, and projecting itself onto the real number axis. The projection on the real axis tells you the waveform's value in real time, while the imaginary parts tell you a forecast of the past and future of the waveform. Voltage and current are each waveforms like this, where they are given in the form of V(t) = A*cos(w*t + phi), where A is the amplitude, w is a term related to the frequency, and phi is the phase shift, from the original cosine function defined as a phase of zero. You can represent this waveform as a complex number, in the form of V = A*e^(i*phi), which in Cartesian form is A*cos(phi) + j*A*sin(phi).
Note: EE's use j for the imaginary unit, because the letter i is spoken-for to stand for current.
Onto the example:
A 60 Hz waveform of 100V amplitude is applied to a 100-Ohm resistor and a 100 millihenry inductor in series. Find the amplitude of current, and the phase shift from the source's voltage waveform.
Resistor impedance: Zr = R
Inductor impedance: ZL = j*w*L
Value of w, for 60 Hz = 2*pi*60 = 377 rad/sec
Thus:
Zr = 100 Ohms; ZL = 37.7 j-Ohms
Find the net impedance of the circuit:
Znet = Zr + ZL
Znet = (100 + 37.7*j) Ohms
Let V have a phase angle of zero, to keep it simple. Use V = I*Z, and solve for I, to find current.
I = V/Z
I = 100V / ((100 + 37.7*j) Ohms)
Carry out the complex number math, and get:
I = (0.876 + 0.330*j) Amps
or in Mod-Arg form:
I = 0.936*e^(-j*0.36) Amps
Amplitude of I = 936 milliamps
Phase angle of I = -0.36 radians, or -20.7 degrees
The negative indicates that current is delayed from voltage, as is expected for an inductor.
@@carultch thank you so, so much for breaking down this example for me. I am not a “math person” as you can see, but I am infinitely curious about the world and often wonder how this kind of maths is applied in our world. You are greatly appreciated. ❤️❤️❤️
@@rakeshbai2732 No problem. Glad I cold enlighten you.
I'd like to have seen more applications of complex numbers when being introduced to them in my math class. Unfortunately, a lot of them require background knowledge that is far beyond the scope of what you are expected to know as a high school student.
The most electrical background you can expect students to know at that point, is maybe the basic relationship among current/voltage/resistance and the two Kirchhoff rules. But who would know what a capacitor or an inductor is? Or the AC specifics?
Too much chatter amongst the students Mr Nice-Guy Eddie.
He's cute
deemorvee theorem
you DO say moue
منو ضربة اليأس من ديموافر وجي هنا 😅😁
ختمت وزارياته و اثرائياته و اجيت ادور مستوى اصعب
Morpheus theoram
Who is here from Linear Algebra?
0:40 r r 😂😂
Who the hell cares about the pronunctuation?
Patrick Borg the French
*pronunciation
People who are particular about using names correctly
OMG is he British
Aussie
is iraq
Ne anlatıyor bu Çinli