Thanks! I really needed this. I´m currently preparing for my bachelor thesis about NMR-Spectroscopy and was stuck on the representation of a oscillations with complex numbers. 7:40 blew my Mind!
@@damianflett6360 sqrt(-1) has no real roots. It makes it worst when you use ijk= -1 You can assign j as sqrt(-1) but then what is i and k? You see the insanity? Only matrix has the real i, j, and k values.
@@lukiepoole9254 you’re confusing quaternions and complex numbers. The two are completely different systems with different applications, which rarely interact, and both of them are perfectly well defined.
If we keep the base as base e, then the rotation rate around the unit circle is such that we travel 1 radian for every 1 unit in the number multiplied by i. If we change the base, then we use the change-of-base rule, and get the following for a general base b: b^(i*theta) = e^(i*theta*ln(b)) This means that it would equal: b^(i*t) = cos(ln(b)*t) + i*sin(ln(b)*t) (Since it's not necessarily equal to an angle, I'll simply call it t) As you can see, this means we change the rotation rate by a factor of the natural log of the base. For 2^(i*t), we get cos(ln(2)*t) + i*sin(ln(2)*t). This means, when t = 1, we only travel about 69% of 1 radian around the unit circle, rather than 1 radian. This means instead of travelling 1 meter, if the unit of the unit circle were meters, that we'd travel 69 cm, and end up at an angle of 0.69 radians or 39.7 degrees. If we wanted to travel a quarter turn, instead of selecting t to equal pi/2, we'd have to select t to equal pi/(2*ln(2)), if we were using 2 as the base of the complex exponential instead of e.
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.
