Equation of a line in complex plane - Physics Forums
May 12, 2013 · The discussion revolves around the derivation of the equation of a line in the complex plane, specifically how the identification of points in the real plane with complex numbers is handled …
'constant' functions on complex analysis • Physics Forums
Jan 10, 2011 · The discussion revolves around the concepts of Liouville's theorem and the maximum principle in complex analysis. Participants explore the implications of these theorems, particularly …
Equation of a Circle in the Complex Plane • Physics Forums
Oct 1, 2013 · A participant provides an explicit expansion of the circle's equation in Cartesian coordinates, showing the transition to the complex form. Several participants reiterate properties of …
Rotations in the complex plane - Physics Forums
Sep 6, 2014 · This discussion focuses on the mathematical concept of rotations in the complex plane using complex numbers. The user accurately describes how multiplying a vector by the imaginary …
Angles between complex vectors - Physics Forums
Mar 31, 2016 · The discussion revolves around finding the angle between two complex vectors in a 4-dimensional space, exploring both Euclidean and Hermitian angles. Participants reference …
Mapping the Unit Disk onto the Complex Plane: A Holomorphic …
Mar 9, 2010 · Participants express disagreement regarding the possibility of a holomorphic mapping from the unit disk to the complex plane, with some arguing against it based on compactness and …
How Do You Perform a 90 Degree Rotation of a Complex Number …
Sep 30, 2008 · A later reply clarifies that the original intent was to rotate the complex plane around the point 2+i, confirming the correctness of the initial approach and providing a combined mapping for …
Why are waves represented as complex numbers? - Physics Forums
Oct 22, 2013 · One participant discusses the application of complex numbers in the context of Maxwell's equations, highlighting their utility in analyzing plane waves and constructing solutions via Fourier …
How to integrate the delta function of complex variable?
Dec 11, 2011 · Another participant offers a generalization of the delta function to the complex plane, expressing it in terms of the sign function and discussing its limitations in selecting marked points …
How to find the equation of a line in complex analysis?
Jan 21, 2009 · The complex plane is simply an imaginary axis and a real axis at right angles to each other. If z = (x, y) = x + iy is an arbitrary complex variable, it pretty much replaces y in our equations …