# Solving rectangular form simultaneous equations?

Hi, I have the following 3 simultaneous equations to solve for the currents I1, I2 and I3:

I1(0-j5) + I1(5+j5) - I3(5+j5) - 20 = 0

I2(5+j5) + I2(0-j10) + I3(0-j10) - 20 = 0

I1(0-j5) + I3(10+j0) - I2(5+j5) = 0

Does anyone have the link to any online software I could use to solve the problem? I have tried solving it by hand but seem to get a bit stuck. Can the I1(0-j5) + I1(5+j5) terms be combined to form 2I1(5) = 10I2 ? Likewise I2(5+j5) + I2(0-j10) = 2I2(5-j5) is this possible?

SteamKing
Staff Emeritus
Homework Helper
The complex coefficients of I2 are just constants. (5+j5)I2 + (0-j10)I2 = (5-j5)I2

The system of equations with complex values can be split up be equating the real part of the coefficients to the real part of the RHS. Similarly for the complex part of the coefficients.

for example, the first equation from the OP can be written:
0 * I1 +5 * I1 - 5 * I3 = 20

-j5 * I1 + j5 * I1 - j5 * I3 = 0

If the first equation is written correctly (it does not contain an I2 term), then

5* I1 - 5 * I3 = 20
-j5* I3 = 0

gneill
Mentor
Hi, I have the following 3 simultaneous equations to solve for the currents I1, I2 and I3:

I1(0-j5) + I1(5+j5) - I3(5+j5) - 20 = 0

I2(5+j5) + I2(0-j10) + I3(0-j10) - 20 = 0

I1(0-j5) + I3(10+j0) - I2(5+j5) = 0

Does anyone have the link to any online software I could use to solve the problem? I have tried solving it by hand but seem to get a bit stuck. Can the I1(0-j5) + I1(5+j5) terms be combined to form 2I1(5) = 10I2 ? Likewise I2(5+j5) + I2(0-j10) = 2I2(5-j5) is this possible?

Sure.

(A + jB) + (C + jD) = (A+C) + j(B+D)

and

(A + jB)(C + jD) = AC - BD + j(AD+BC)