# Solving systems of equations that contain complex numbers

1. Dec 18, 2016

### Cocoleia

1. The problem statement, all variables and given/known data
I am having trouble solving systems of equations when they contain complex numbers. The context is circuit theory and phasors. For example, I am given this

And the goal is to find I2 and Voc, which you can see the answers for. I just don't know how to manipulate the numbers to get to this answer. Can someone explain the steps given these equations?

2. Dec 18, 2016

### Staff: Mentor

You can convert the values with angles to complex values with real and imaginary part as well, and then solve in the same way you would do it with real numbers.

3. Dec 18, 2016

### Ray Vickson

In vector-matrix form, your equations read as
$$\pmatrix{600-300j&300j&0\\-300j&300+300j&-2\\300j& -300j&1} \pmatrix{I_1\\I_2\\V} = \pmatrix{9\\0\\0}$$.
This is just an ordinary 3x3 linear system, that you can solve using Gaussian elimination or matrix inversion or row-reduction---all standard elementary algebra methods. (The only difference is that you need to use complex arithmetic instead of real arithmetic.)

When I solve this system using Maple I get a solution much different from the one you propose.

4. Dec 18, 2016

### Cocoleia

These were the answers given to us by the professor. They could be wrong. But thanks, I will try to solve it like that