Do complex numbers really exist? - Mathematics Stack Exchange
Complex numbers are the final step in a sequence of increasingly "unreal" extensions to the number system that humans have found it necessary to add over the centuries in order to express significant numerical concepts. The first such "unreal number" was zero, back in the mists of time.
complex numbers - Why is $ |z|^2 = z z^* $? - Mathematics Stack …
2014年5月9日 · The identity was presented to me baldly along with a sloppy explanation to complex numbers back when I took my intro class. Unfortunately, not all educators are able to present mathematics in an accessible, intuitive way. That's a real skill. $\endgroup$ –
Difference between imaginary and complex numbers
$\begingroup$ It should be added that in modern mathematics there is almost never any reason to talk about imaginary numbers in general -- just about everything you can say about imaginary numbers is just as valid about all the complex numbers, so it is usually said in that more general form. $\endgroup$ –
"Where" exactly are complex numbers used "in the real world"?
2013年1月24日 · $\begingroup$ There are plenty of applications of complex numbers, but from what I have seen they are typically used to simplify solving a math equation, and the end result is still a real number. Or in some cases (lile quantum) a 2d vectors are represented with complex numbers, but could be represented with 2d vectors.
How Do I Understand $e^i$, the Euler Form of Complex Number
2013年2月18日 · Each complex number is assigned a magnitude and an angle (called the argument). This is done precisely with the complex exponential. You may recall that multiplying two complex numbers is equivalent to rotating one number by the angle of the second (and then applying the proper stretches and compressions).
Positive and negative complex numbers? - Mathematics Stack …
2014年5月10日 · A complex number can be treated as a kind of multivector existing in a 2-d geometric algebra (GA). Seen this way, the answer to your question is that you can indeed negate complex numbers, much in the same way that multivectors (or …
complex numbers - De Moivre Theorem for Fractional Power: k
In other words, we can simplify the multiplication of complex numbers to $$(r,\theta)\times(s,\alpha)=(rs,\theta+\alpha).$$ A lot more elegant in my opinion than the standard approach! De Moivre's Theorem. This work makes De Moivre's Theorem very straightforward indeed. De Moivre's Theorem for Natural Number Powers
Can a complex number ever be considered 'bigger' or 'smaller' …
2015年1月23日 · It would seem that the 'sizes' of numbers of any type (real, rational, integer, natural, irrational) can be compared, but once imaginary and complex numbers come into the picture, it becomes a bit counter-intuitive for me. So, does it ever make sense to talk about a real number being 'more than' or 'less than' a complex/imaginary one?
Complex power of a complex number - Mathematics Stack Exchange
complex-numbers; Share. Cite. Follow asked Aug 27, 2013 at 2:19. Johnny Apple Johnny Apple. 4,483 2 2 gold ...
Why do complex numbers lend themselves to rotation?
2023年7月7日 · First of all, complex numbers are two-dimensional, having independent x (real) and y (imaginary) components. This makes it possible to define a “rotation”, which you can't really do with one-dimensional real numbers (unless you count flipping the sign). However, this property isn't unique to complex numbers.
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