# Solving systems of equations that contain complex numbers

## Homework Statement

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?

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mfb
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.

Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

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
View attachment 110531
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?
$$\pmatrix{600-300j&300j&0\\-300j&300+300j&-2\\300j& -300j&1} \pmatrix{I_1\\I_2\\V} = \pmatrix{9\\0\\0}$$.
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.

$$\pmatrix{600-300j&300j&0\\-300j&300+300j&-2\\300j& -300j&1} \pmatrix{I_1\\I_2\\V} = \pmatrix{9\\0\\0}$$.