# Mathematica: Solving Linear Complex Systems

1. Nov 7, 2012

### BLUE_CHIP

Good evening,

I am currently trying to use Mathematica to find the symbolic solutions to a set of complex linear equations. I have never used Mathematica for such a task before and am finding it quite difficult. Let me state the problem:

$$\begin{pmatrix}a^{*}a-b^{*}b&ac^{*}-bd^{*}\\a^{*}c-b^{*}d&c^{*}c-d^{*}d\end{pmatrix}=\begin{pmatrix}-(\mu+2tcos(p))&2(\Re(\Delta)-i\Im(\Delta))sin(p)\\2(\Re(\Delta)+i\Im(\Delta))sin(p)&\mu+2tcos(p)\end{pmatrix}; \qquad \text{ where } \mu, \Re(\Delta), \Im(\Delta), t \text{ are real constants }; p\inℝ$$

I am attempting to solve for the complex functions $$a(p), b(p), c(p), d(p)$$ Is this even possible or am I wasting my time?

Thanks

2. Nov 7, 2012

### Bill Simpson

By inspection, assuming your j(delta) is not equal to zero, that sin(p) is equal to zero.

That substantially simplifies your task, but, like many things in Mathematica, at the moment it is resisting doing something that is simple to describe.

Last edited: Nov 7, 2012
3. Nov 8, 2012

### BLUE_CHIP

This problem has been solved.

Thank you.