# Thread: System of equations with complex numbers

1. ## System of equations with complex numbers

What's the easiest or fastest way to solve system of equations with complex numbers.For example how would you solve this system?
25x+(25-j50)y+(25+j100)z=j20
(25-j50)x+(125-j100)y+(25-j50)z=0
(25+j100)x+(25+j50)y+(225+j200)z=60+j80
x,y,z are complex.

2. ## Re: System of equations with complex numbers

Originally Posted by Garas
What's the easiest or fastest way to solve system of equations with complex numbers.For example how would you solve this system?
25x+(25-j50)y+(25+j100)z=j20
(25-j50)x+(125-j100)y+(25-j50)z=0
(25+j100)x+(25+j50)y+(225+j200)z=60+j80
x,y,z are complex.
The same way you would solve any system of equations really, multiply each equation by an amount that equates the coefficients of one of the variables, so that you can eliminate that variable from two of the equations. Follow this process until you have upper-triangularised the system so that you can solve for each variable.

I would start by multiplying the second equation by $\displaystyle (25 + 50j)$ and the third equation by $\displaystyle (25 - 100j)$, at least then the coefficients of x will be real...

3. ## Re: System of equations with complex numbers

It works fine with real numbers but you cannot use gauss method to solve complex equations because you cannot eliminate variable from two other equations.I read somewhere that you can solve two real system instead of one complex in order to solve that complex but i dont know how to implement that.

4. ## Re: System of equations with complex numbers

Originally Posted by Garas
It works fine with real numbers but you cannot use gauss method to solve complex equations because you cannot eliminate variable from two other equations.I read somewhere that you can solve two real system instead of one complex in order to solve that complex but i dont know how to implement that.
Did you follow my advice? I advised you to multiply the second and third equations by the conjugate of its respective x coefficient. THIS MAKES THE COEFFICIENT REAL, which means you can eliminate them. Once you have eliminated them, do the same thing with the y coefficients, make them real by multiplying by the conjugates, then eliminate.