1. ### Argument of a complex expression

Problem Statement: What is the correct way of computing the argument of the following equation? Relevant Equations: I am trying to compute the argument ##\Phi## of the equation $$\frac{r-\tau\exp\left(i\varphi\right)}{1-\tau r\exp\left(i\varphi\right)} \tag{1}$$ which using Euler's equation...

4. ### Contour Integration over Square, Complex Anaylsis

Homework Statement Show that $$\int_C e^zdz = 0$$ Let C be the perimeter of the square with vertices at the points z = 0, z = 1, z = 1 +i and z = i. Homework Equations $$z = x + iy$$ The Attempt at a Solution I know that if a function is analytic/holomorphic on a domain and the contour lies...
5. ### Solving Schrodinger's Equation with a weak Imaginary Potential

Homework Statement A particle of energy E moves in one dimension in a constant imaginary potential -iV where V << E. a) Find the particle's wavefunction \Psi(x,t) approximating to leading non-vanishing order in the small quantity \frac{V}{E} << 1. b) Calculate the probability current density...
6. ### Complex equation

The problem I would like to solve: $$\bar{z} = z^n$$ where ##n## is a positive integer. The attempt ## z = r e^{i \theta} \\ \\ \overline{ r e^{i \theta} } = r^n e^{i \theta n} \\ r e^{-i \theta} = r^n e^{i \theta n} ## ## r = r^n \Leftrightarrow true \ \ if \ \ n=1 \ \ or \ \ r=1## ##...
7. ### I Need a help in solving an equation (probably differentiation

I am trying to find out the interference condition between tool and a part. The below attached snapshot is the equation between interference and machine feed. At dy/dx = 0, I will have max. interference, which I intend to find. Except x and y every alphanumeric character in the following...
8. ### B Square root of a negative number in a complex field

Mod note: Fixed all of the radicals. The expressions inside the radical need to be surrounded with braces -- { } (This question is probably asked a lot but I could not find it so I'll just ask it myself.) Does the square root of negative numbers exist in the complex field? In other words is...
9. ### Z^4=-80i or general z^n=a+bi

Homework Statement I just cant seem to get the right answer. z^4+80i=0 looking at the complex plane u see the radius=r=80 (obviously) using De Moivre extension: z^n=(r^(1/n))(cos((x/n)+k2pi/n)-isin((x/n)+k2pi/n) z1=((80)^(1/4))(cos(3pi/8)+isin(3pi/8) shouldnt this be a root? z2=...
10. ### Solving z^2+pz+qiz+a+bi=0

ok having major problems. i can easily solve z^2 + pz +a+bi=0 solutions but that extra qiz is really annoying me. z^2 + 3z+4iz-1+5i=0 (z+2i)^2+3z-5+5i=0 z+2i = w, z=w-2i w=-3(w-2i)+5-5i then im not getting anything sensible for solving x and yi. what am i doing wrong?