# Solving a system of complex numbers

• November 1st 2009, 03:02 PM
Oblivionwarrior
Solving a system of complex numbers
I can't seem to figure out this system of complex numbers, the method I am trying is taking way too long. Is there any quicker way? (doing it by hand, solving for X and Y)

$\frac{X}{10} + \frac{X-Y}{5 + 15i} = 1$

$\frac{Y}{-10i} + \frac{Y-X}{5+15i} = 0.866+0.5i$

EDIT: Sorry this probably should have gone in Linear Algerba
• November 2nd 2009, 09:47 AM
Oblivionwarrior
anyone?
• November 2nd 2009, 10:28 AM
Ruun
This is a linear equation for some $x,y \in \mathbb{C}$ so you know that the solution will be a line, this is, the solution will have dimension 1 (why?). Now, solving
$
\frac{x(5+15i)+10x-10y}{10(5+15i)}=1$

$\frac{x(15+15i)-10y}{10(5+5i)}=1$

$x(15+15i)-10y=10(5+5i)$

$x=\frac{10(5+5i)+10y}{15+15i}$