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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...
Why are There No "Triernions" (3-dimensional analogue of complex ...
Since there are complex numbers (2 dimensions) and quaternions (4 dimensions), it follows intuitively that there ought to be something in between for 3 dimensions ("triernions"). Yet no one uses...
"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 ...
To find a square root of a given complex number z z, you first want to find a complex number w w which has half the argument of z z (since squaring doubles the argument).
What free tools can I use to plot complex functions on the complex ...
What free tools can I use to plot complex functions on the complex plane? Ask Question Asked 8 years, 10 months ago Modified 3 years, 10 months ago
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?
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).
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