This is just a few minutes of a complete course. Get full lessons & more subjects at: www.MathTutorDV.... In this lesson the student will learn about complex numbers and how to work with them in trigonometry and precalculus.
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Back in 90's If I had at least one teacher like you , I would not have taken a round about way to robotics. I am into software development but I really enjoy making things. I hope its not to late to start to fill in the gaps of knowledge I have had due to lack of concentration in my teenage and which is because I am a learner who loves to apply things I learn to find solutions to real life problems. So what I am looking forward in your upcoming videos is how you relate the knowledge we gather by following your classes with current usage of it in industry at least in your domain i.e. electrical and electronics. Thanks a lot. I can't express how delighted I am to listen to your lectures.
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I am an engineer and I explain complex numbers in a different REAL manner. Many mathematicians used to send their students to me to explain the engineering operation of complex numbers. The operation is REAL and not imaginary. I am going to use j and not i. When we say " real numbers" we mean to refer to " real operators". that would amplify the entities we are dealing with. Hence, 1,2,3,4,5,6,7,8 are real numbers as in 6 cows, or 5 boxes. Now " j", which mathematicians call an imaginary number, is no imaginary operation, but it is A ROTATIONAL OPERATION OF 90 DEGREES ORIENTATION. All this comes about by the operation which is required to find the SQUARE ROOT OF A NUMBER, BUT NOW WE MUST DESCRIBE, " THE ENGINEERING ACTIVITY/PROCESS THAT ACHIEVES THE SQUARE ROOT OF AN OPERATION" and not just the square root of a number. So here we go in real terms, Defining the SQUARE ROOT OF AN OPERATION, AS, ANOTHER OPERATION WHICH WHEN MULTIPLIED BY ITSELF WILL RESULT IN THE FIRST OPERATION. If the first operation is a real amplification operation of 9, then the square root of 9 is 3, as 3 multiplied by 3 is 9. That of 4 is 2 as 2 multiplied by 2 is 4. If the first operation is a real amplification operation of 1, then the square root of 1 is 1, as 1 multiplied by 1 is 1. Now (minus 1), or (-1) happens to be 1 operated upon by a real rotation by 180 degrees or two ( 90 ) degrees rotations. Note that we are now dealing with rotational operations and not an amplification process. Having defined the SQUARE ROOT OF AN OPERATION, AS ANOTHER OPERATION WHICH WHEN MULTIPLIED BY ITSELF WILL RESULT IN THE FIRST OPERATION. then the square toot of (-1) is A ROTATION OF 90 DEGREES ON A LENGTH OF MAGNITUDE 1. The operation of the sequence is as follows let us take 1 as pointing to the East. (1), rotated by 90 degrees, becomes North, and then, rotated again by 90 degrees, becomes West or (minus one)= (-1). Hence (-1) is brought about by (1) being rotated twice by an angle of 90 degrees which we called (j) Note that we add rotational degrees when we multiply the vectors. So the operator j is not an imaginary number and it is now to be called just the square root of minus one, but it is a real rotational operation of 90 degrees to any entity placed beside it. The square root of (-1) is one rotation of 90 degrees The square root of (-4) is one rotation of 90 degrees to the real number 2, written a j2 The square root of (--9) is one rotation of 90 degrees to the real number 3, written as j3 IT IS ALL REAL ENGINEERING OPERATIONS AND IT IS THESE ROTATIONS THAT LEAD TO OSCILLATIONS found in repetitive heartbeats, musical frequencies, ballet pirouette dancing, and rotations of shafts and propellers, steam, diesel, and petrol engines and jet turbines, and electronic oscillations, spinning wheels it is all REAL! Please, Stop calling (j) an imaginary number, as the square root of (-1) is a real operation of 90 degrees rotation. Real Numbers may be looked upon as amplifiers, with no phase change. j operator may be looked upon as a rotation of 90 degrees. (3+j4) is an amplifier with a phase shift e^(3+j4)t is a spiraling vector that is growing in magnitude as (e^3t) and rotating as (e^jwt) e^jwt = cos(wt) + jsin(wt) t= time variable, w = angular rotation, j= one 90 degreees rotoation. All the above activities are real engineering processes found in many machines found inside and outside our homes bringing with them all the tangible and guaranteed comforts of our life, there is nothing imaginary about that.
Hello, i paid for the lessons and they are great. But am looking for the continuation of complex numbers where the de Moivres theorem and polar form and complex numbers with powers, i cant find it. help with this please. i have already sent an email. thanks
I want to buy a subscription in your website, but turn out it requires a credit card which I cannot afford at this moment, I only have PayPal. Also, could you update your site to looks a little bit more modern? Thank you!
What I wonder here is why didn't mathematicians multiply -1 to the square root instead of using imaginary 'i' , so inherently a square root of something negative will have a -1 multiplied. (time - 4:49). Why define it as sqrt(-1) instead directly as -1. Is there a requirement to fulfil some other conditions.
why do maths teachers start with the muddles of history instead of basic concepts? complex numbers are points on a plane; they are vectors. nothing imaginary about them at all.
