help with solving equations with complex values and or phasors

[Anders]

For a linear system of 3 equation with 3 unknowns (x, y, z), you can simply use matrix math (works also for complex coefficients and variables). Normalize the equations with the variables and coefficients on the left side of the = sign and the constant on the right side of the equal sign on paper first with all variables in the same order for all equations. Then Put the left hand side coefficient in a 3x3 matrix (just call it M1 for simplicity) and the right hand side values into a vector (say M2) and then simply do M1^-1 * M2 and then you have (x y z) in the resulting vector. You can do this directly in home view using [] function.

Example:
Lets say you have the following 3 equations:
(1+i)x + (3+i)y + (4-2i)z = 2i
(1+2i)x + (2+2i)y + (3+i)z = 3+i
1x+ iy +4iz = 1
A matrix for the left hand side and a vector for the right hand side on the form AX=B, where A is 3x3 matrix of al the coefficients and X is the (x,y,z) vector and B is the right hand side constant vector.
Multiply with the inverse of A on both side and you get X= A^(-1) * B.
See the screen capture below. The result is the (x,y,z) vector, i.e.
x= (-12-55i)/13, y = (7+69i)/13, z = (25-47i)/26
if you press blue shift Enter then you get the approximate value of x,y,z.
You can do this for larger or smaller systems as well, e.g. for a 4 variable and 4 equation system A is a 4x4 matrix and B is a 4x1 vector of the right hand constants.