Oct 6, 2017 · 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 …

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.

Jul 7, 2023 · 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 …

Jan 10, 2013 · So in that sense, one could see complex numbers as a more elegant 'data structure' to do Fourier transforms with?

Sep 13, 2020 · The 3-dim complex numbers that I propose here commute, and many have an inverse. I don't know if they are associative and if they accept a matrix representation like complex numbers, …

Jan 24, 2013 · 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 …

Nov 8, 2019 · This is a follow-up to a previous question regarding complex numbers. Many people there compared complex numbers to vectors, and there was disagreement about what the difference was. …

Feb 14, 2013 · A complex number z is an order-pair of real numbers (x, y) where we call x the real part of z and y the imaginary part of z. For x = 0 and y = 1, we denote z as i.

This is one of the main reasons complex numbers are so important; they are the algebraic closure of the real numbers. You will never need "higher levels" of imaginary numbers or new mysterious square …

@Shashaank as any vector in Cn C n over C C is an n-tuple of complex numbers, it is exactly the complex number i i, in the first entry of this n-tuple. In the case being discussed, n = 2 n = 2, but in …