# Solving complex equation

## Homework Statement

(2+5i)/(x-y)-(1-3i)/(x+y)=-7x+12i/y(square)+x(square)

## Homework Equations

I only know the result to be x=-5/14 y=-1/14

## The Attempt at a Solution

If you could only lead on how to proceed I would be grateful
Xbtw is there any software that could solve the above equation ?

Mathematica would solve that sort of equation just fine. So would Maple and Matlab for that matter. www.wolframalpha.com would also suffice. As for solving it by hand, I dont see any clear way to do it without a whole lot of work.

epenguin
Homework Helper
Gold Member
On the left hand side express as a single fraction, which involves multiplying the denominators, which gives denominator (x2 - y2), unfortunately not quite the same as a denominator appearing on the right-hand side - and I wonder whether you have transcribed it properly, whether it is not really 12i/(y2 + x2). If it is that, you can combine those two bits into (something)/(x4 - y4). Whether it's that or really ...+ 12i/y2 +... still combine into one fraction. In the end express the whole thing with a single denominator. Numerator = 0 gives you solutions but watch out whether enumerator and denominator have common factor which=0 is not a solution of problem.

You being stuck suggests you probably need to revise adding/subtracting fractions, you may need to revise how to deal with expressions with complex numbers - here nothing needed except work like with real numbers but just whenever you get i2 it becomes -1.

I haven't done it and don't know whether any significant simplifications come up; it is some work but a quite routine problem.