Solving simultaneous equations with imaginary numbers

Question

Consider the following simultaneous equation:

$$\begin{cases} 5z-(3+i)w=7-i\\ (2-i)z+2iw = -1+i \end{cases} $$

What is the simplest way to manipulate one of the equations so that a variable can be eliminated and the equation solved?

Answer 1

You do it the same way you do it over the reals. For example, you could solve the first equation for $z$, $z=(7-i+(3+i)w)/5$, substitute that into the 2nd equation, solve for $w$, then get $z$. Or, multiply the first equation by $2-i$, the second by 5, and subtract to eliminate $z$.