I encounter systems of linear complex equations (At most 3 equations) in my circuit analysis course.
The calculator I am using is Casio fx-991ES and it only accepts real elements when in matrix or equation solver mode.
So, is there a way to manipulate a matrix so that there are no $j$'s left in it?
The only solution I found was replacing each element $a+bj$ with a 2 by 2 matrix.
\begin{array}{ccc}
a & -b\\
b & a \\
\end{array}
but then the matrix dimensions will be doubled making a 2×2 matrix a 4×4 matrix. which unfortunately exceeds the casio 3×3 limit for maximum matrix size.
The only other solution is using Cramer's rule which works well for 2×2 matrices but gets really messy for 3×3.
So, is there a solution from the theoretical side other than those two ?
If not would you please suggest a calculator that is capable of solving complex equations? my college's policy is so strict regarding this matter all graphing and sophisticated programmable calculators are not allowed. If there is a calculator close to 991ES that would be great.
Thanks in advanced.
Best Answer
You could try storing two separate matrices for the real and imaginary components. So for example, $$ \pmatrix{ 1 + j & 2-j\\ 4 & 3j } = \pmatrix{ 1&2\\4&0 } +j\pmatrix{ 1 & -1\\0 &3 } $$ Suppose that $M = A + jB$ and $N = C + jD$. It would follow that $$ MN = (A + jB)(C + jD) = (AC - BD) + j(AD + BC) $$