The problem involves finding the real solutions for a complex equation represented as (4+2i)x + (5-3i)y = 13+i, which falls under the subject area of complex numbers and simultaneous equations.
The discussion is active with participants attempting to clarify their understanding of the problem setup. Some guidance has been provided regarding the necessity of equating both real and imaginary parts to find solutions. Multiple interpretations of the approach are being explored without explicit consensus.
There is an indication of uncertainty regarding the correctness of initial methods and the interpretation of the problem, as well as a focus on ensuring that both parts of the equation are satisfied for real solutions.
The above is correct.NewtonianAlch said:Homework Statement
Find the real solutions of
[itex]\left( 4+2\,i \right) x+ \left( 5-3\,i \right) y=13+i[/itex]
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.
No. you are looking for the real solutions for x and y, which make the complex equation true.Would I then only consider the real part and solve that?
This is correct.NewtonianAlch said: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?