My circuits analysis textbook teases that there's a way to convert a set of n complex equations into a set of 2n real equations, which can then be solved using any calculator that can solve real simultaneous equations. That is, no capability with complex numbers needed.
e.g.:
$(25 +j100)I_1 – (10+j80)I_2=100\angle0^\circ\\$ (1)
$-(10+j80)I_1+(30+j190)I_2=0$ (2)
I say "teases" because they point me to their website, where after a lengthy sign-up process, I find that the material isn't actually there.
Does anybody know what method they're referring to?
I know how to do this with Cramer's Rule, but that requires a matrix calculator that understands complex numbers (they exist but they're not common).
Here's the page:
Best Answer
The main idea is to split each equation into a real and a complex part.
To easily see how to do this take a look at complex multiplication as a linear transformation.
$(a + bi) * (c + di) = (ac - bd) + (bc + ad)i$ will become
$\left(\begin{array}{cc}c&-d\\d&c\end{array}\right) \left(\begin{array}{c}a\\b\end{array}\right)= \left(\begin{array}{c}ac-bd\\bc+ad\end{array}\right)$
You can use this pattern to rewrite your example as
$\left(\begin{array}{cccc|c} 25&-100&-10&80&100\\ 100&25&-80&-10&0\\ -10&80&30&-190&0\\ -80&-10&190&30&0 \end{array}\right)$