The formula is decomposed into two components sinw and cosine. Real and imaginary parts. It is related to trigonometric relationships and the relationship between polar and cartesian coordinates.
Complex numbers are fake invented math because (1) the definition of a complex number contradicts to the laws of formal logic, because this definition is the union of two contradictory concepts: the concept of a real number and the concept of a non-real (imaginary) number-an image. The concepts of a real number and a non-real (imaginary) number are in logical relation of contradiction: the essential feature of one concept completely negates the essential feature of another concept. These concepts have no common feature (i.e. these concepts have nothing in common with each other), therefore one cannot compare these concepts with each other. Consequently, the concepts of a real number and a non-real (imaginary) number cannot be united and contained in the definition of a complex number. The concept of a complex number is a gross formal-logical error; (2) the real part of a complex number is the result of a measurement. But the non-real (imaginary) part of a complex number is not the result of a measurement. The non-real (imaginary) part is a meaningless symbol, because the mathematical (quantitative) operation of multiplication of a real number by a meaningless symbol is a meaningless operation. This means that the theory of complex number is not a correct method of calculation. Consequently, mathematical (quantitative) operations on meaningless symbols are a gross formal-logical error; (3) a complex number cannot be represented (interpreted) in the Cartesian geometric coordinate system, because the Cartesian coordinate system is a system of two identical scales (rulers). The standard geometric representation (interpretation) of a complex number leads to the logical contradictions if the scales (rulers) are not identical. This means that the scale of non-real (imaginary) numbers cannot exist in the Cartesian geometric coordinate system.
I'm a (retired) electronic engineer and we use complex numbers all the time to solve real problems. Yes, they are an artificial mathematical construction, but no more so than negative numbers. Think about it: you can't have -3 apples any more than √-1 apples. The thing about complex numbers is that they are stepping stones that allow us to start with a real engineering problem, do some complex arithmetic and then to convert the result back into a real result that can be applied to the problem. There's always a way to solve such problems without using complex numbers, but using them makes the maths much simpler. For example, using complex numbers allows us to handle two coordinates at the same time. If you wanted to avoid complex numbers, then you'd need to do two separate calculations. Using complex numbers to represent two dimensions works really well, even though imaginary numbers don't actually exist. Maths is full of such artificial ideas, for example 0! (0 factorial), ∞, etc. If you want an even weirder idea, look at p-adic numbers.
@chrisengland5523 Sorry, I saw your comment now. The software you use doesn't use imaginary numbers. It uses vector analysis. It's simple to check it.
Good video very informative 👍
But how does e comes into picture?
The formula is decomposed into two components sinw and cosine. Real and imaginary parts. It is related to trigonometric relationships and the relationship between polar and cartesian coordinates.
A guy calculated that ix=ln(cosx + isinx) Euler then exponentiated it
😀
Can you please explain why you depict i (imaginary unit) equal to 1 (real unit)? Is it i=1? I thought i=sqrt(-1).
You are right i= sort (-1)
@@amromohamedelfeki8045 So, if i=sqrt(-1) why do you depict it equal to 1?
@@amromohamedelfeki8045 Well? Do you have an answer or no? Are you stating that sqrt(-1)=1?
I did not depict i equal 1
@@amromohamedelfeki8045Seriously now? Right at the beginning you depict i on the top side (y axis) of a circle and on the x axis it's shown 1.
Complex numbers are fake invented math because
(1) the definition of a complex number contradicts to the laws of formal logic, because this definition is the union of two contradictory concepts: the concept of a real number and the concept of a non-real (imaginary) number-an image. The concepts of a real number and a non-real (imaginary) number are in logical relation of contradiction: the essential feature of one concept completely negates the essential feature of another concept. These concepts have no common feature (i.e. these concepts have nothing in common with each other), therefore one cannot compare these concepts with each other. Consequently, the concepts of a real number and a non-real (imaginary) number cannot be united and contained in the definition of a complex number. The concept of a complex number is a gross formal-logical error;
(2) the real part of a complex number is the result of a measurement. But the non-real (imaginary) part of a complex number is not the result of a measurement. The non-real (imaginary) part is a meaningless symbol, because the mathematical (quantitative) operation of multiplication of a real number by a meaningless symbol is a meaningless operation. This means that the theory of complex number is not a correct method of calculation. Consequently, mathematical (quantitative) operations on meaningless symbols are a gross formal-logical error;
(3) a complex number cannot be represented (interpreted) in the Cartesian geometric coordinate system, because the Cartesian coordinate system is a system of two identical scales (rulers). The standard geometric representation (interpretation) of a complex number leads to the logical contradictions if the scales (rulers) are not identical. This means that the scale of non-real (imaginary) numbers cannot exist in the Cartesian geometric coordinate system.
Thanks for your comment. I consider imaginary numbers as a mathematical trick to solve some engineering problems.
@@amromohamedelfeki8045 Yes. A trick that leads to gross errors.
I'm a (retired) electronic engineer and we use complex numbers all the time to solve real problems. Yes, they are an artificial mathematical construction, but no more so than negative numbers. Think about it: you can't have -3 apples any more than √-1 apples.
The thing about complex numbers is that they are stepping stones that allow us to start with a real engineering problem, do some complex arithmetic and then to convert the result back into a real result that can be applied to the problem. There's always a way to solve such problems without using complex numbers, but using them makes the maths much simpler. For example, using complex numbers allows us to handle two coordinates at the same time. If you wanted to avoid complex numbers, then you'd need to do two separate calculations. Using complex numbers to represent two dimensions works really well, even though imaginary numbers don't actually exist.
Maths is full of such artificial ideas, for example 0! (0 factorial), ∞, etc. If you want an even weirder idea, look at p-adic numbers.
@chrisengland5523 Sorry, I saw your comment now. The software you use doesn't use imaginary numbers. It uses vector analysis. It's simple to check it.