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.

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...

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 …

Complex power of a complex number [closed] Ask Question Asked 12 years, 4 months ago Modified 9 months ago

May 9, 2014 · 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?

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).

Jan 30, 2015 · 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 …

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 …

Jun 16, 2021 · Then 1 + i 1 + i is both an equation that shows how to "get" from real and imaginary numbers to complex numbers, and a representation of the final complex number itself.