# Homework Help: Simultaneous equation with Complex Numbers

1. Jul 25, 2011

### Jake2954

Solve the following simultaneous equations for the complex variables i1 and i2.

2= (3-j)i1 - (5-j2)i2………………(1)
12 = (2+j)i1 + (1+j6)i2………………(2)

Not sure how to attempt this question please can you help.

Jake
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 25, 2011

### tiny-tim

Welcome to PF!

Hi Jake! Welcome to PF!

Solve it the same way you would for real simultaneous equations

(and use eg 1/(3-j) = (3+j)/(32-j2))

3. Jul 25, 2011

### Jake2954

t-t Please excuse my ignorance but I am learning out of a book and need a push in the right direction. Is it possible to show me step by step the correct approach as my head is spinning.

4. Jul 25, 2011

### tiny-tim

Sorry, Jake, this forum doesn't work that way.

Show us how you would solve this if all the coefficients were real.

5. Jul 25, 2011

### Jake2954

Well the approach I would use is to make either i1 or i2 equal on line 1 + 2 by multiplying by the value of the opposite lines. Lets call them now line 3 + 4. Then I would subtract 4 from 3. This would leave only 1 unknown.

6. Jul 25, 2011

### Jake2954

Still don't understand can anyone else help?

7. Jul 25, 2011

### Dickfore

It's a linear system of 2 equations with two variables. You can use the method of determinants (Cramer's rule). One determinant is:

$$\Delta = \left|\begin{array}{cc} 3 - j & 5 - 2 j \\ 2 + j & 1 + 6 j \end{array}\right| = (3 - j)(1 + 6 j) - (2 + j)(5 - 2 j) = 3 + 18 j - j - 6 j^2 - 10 + 4 j - 5 j + 2 j^2 = -3 + 16 j$$