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complex numbers - Parametrizing shapes, curves, lines in $\mathbb {C ...
I've been struggling with parametrizing things in the complex plane. For example, the circle |z − 1| = 1 | z 1 | = 1 can be parametrized as z = 1 +eiθ z = 1 + e i θ.
What is the dot product of complex vectors?
This complex "dot product" is sometimes called a Hermitian form. This specific separate term serves as a way to make it clear that it might not comply with the usual definition of a dot product, if you don't generalize that definition as shown above.
Do complex numbers really exist? - Mathematics Stack Exchange
Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obviou...
"Where" exactly are complex numbers used "in the real world"?
50 Complex numbers are used in electrical engineering all the time, because Fourier transforms are used in understanding oscillations that occur both in alternating current and in signals modulated by electromagnetic waves.
radicals - How do I get the square root of a complex number ...
The square root is not a well defined function on complex numbers. Because of the fundamental theorem of algebra, you will always have two different square roots for a given number.
Defining the equation of an ellipse in the complex plane
Application If you are an engineer like I am, you are probably thinking of these equations in terms of phasors, which are complex numbers with fixed magnitude and linear phase (their phase changes at a constant rate). We are in the business of turning real signals into complex phasors for DSP applications.
complex numbers - Why is $ |z|^2 = z z^* $? - Mathematics Stack Exchange
I've been working with this identity but I never gave it much thought. Why is $ |z|^2 = z z^* $ ? Is this a definition or is there a formal proof?
Why do complex numbers lend themselves to rotation?
In the introductory complex analysis course I am taking, nearly every theorem relates to rotation and argument. Why do complex numbers love doing this so much? I can understand why these theorems w...
Why is the complex number - Mathematics Stack Exchange
That is, the collection of complex numbers is a two-dimensional real vector space, and multiplication by a + bi a + b i is a real-linear map of C C to itself, so, with respect to any R R -basis of C C, there'll be a corresponding matrix.
Easy example why complex numbers are cool - Mathematics Stack Exchange
I am looking for an example explainable to someone only knowing high school mathematics why complex numbers are necessary. The best example would be possible to explain rigourously and also be clea...
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