# Find the real solutions

1. Apr 12, 2012

### NewtonianAlch

1. The problem statement, all variables and given/known data
Find the real solutions of

$\left( 4+2\,i \right) x+ \left( 5-3\,i \right) y=13+i$

3. The attempt at a solution

4x + 2xi + 5y - 3yi = 13 + i

4x + 5y - 13 + i(2x -3y - 1) = 0

I am not really sure if my method is correct here for starters.

Would I then only consider the real part and solve that?

2. Apr 12, 2012

### SammyS

Staff Emeritus
The above is correct.

No. you are looking for the real solutions for x and y, which make the complex equation true.

In order for a complex equation to be true, the real part of the right side must equal the real part of the left side AND the imaginary part of the right side must equal the imaginary part of the left side

3. Apr 12, 2012

### NewtonianAlch

I'm not entirely sure what you mean, but I think

4x + 5y = 13 and 2x -3y = 1 ?

So it's just a simultaneous equation, and solving for x and y gives us real solutions. Is that it?

4. Apr 12, 2012

### NewtonianAlch

Anyone know if this is right?

5. Apr 12, 2012

### SammyS

Staff Emeritus
This is correct.

4x + 5y - 13 + i(2x -3y - 1) = 0 :​

Equating the real parts gives:
4x + 5y - 13 = 0 .​

Equating the imaginary parts gives:
2x -3y - 1 = 0 .​

That's what I mean.

6. Apr 12, 2012

### NewtonianAlch

Damn...thanks.