Good evening,
Summing up the problem I have is the following:
Is it possible to have complex numbers in a System of Linear Equations?
It is hard for me to visualize this problem as well, since if we have a System of Linear Equations with, for example, three unknowns and three equations, it is possible to find the relationship between those three equations of lines. Visualizing this is doable as well.
But, trying to do this with complex numbers is confusing me. I do think it is possible but an approach is not coming to mind.
Kind regards,
Tema.
Best Answer
Yes, you can have sets of complex linear equations. For instance, $$ \cases{(5+3i)x+(2-i)y=1\\(-7+4i)x+(8+9i)y=4-3i} $$ Yes, it's difficult to visualise. This one in particular requires you to see in your mind's eye two planes in four-dimensional space, and find their intersession point. And it doesn't get easier for higher number of unknowns.
However, the algebra doesn't care. You solve this more or less exactly the same way you would solve a set of two real equations in two variables. Get rid of one variable through either substitution, or adding some suitable multiple of one equation to the other equation, then solve for the other variable.