Can Complex Equations Be Solved Using Software?

[lorik]

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 ?

 

[inutard]

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 don't see any clear way to do it without a whole lot of work.

 

[epenguin]

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.