How do you work out simultaneous eqns w/ complex numbers & phasor

[whatphysics]

I'm having trouble figuring out to get the answers from the 2 equations. The phasors and complex numbers confuse me. Do I need to change the phasor form? How do I go about doing this thanks! (Not homework question I am trying to figure this for my exam!)

 

[Simon Bridge]

There are lots of ways to do this sort of problem ...
For complicated meshes, you may find it easier to convert to complex impedences and use a+jb type notation.
So 20∠0 would be just 20+0j, 20∠π/2 would be 0+20j (j=√-1). Then you can solve the simultaneous equations normally.

For simple problems you can usually just add the phasors like vectors.

 

[The Electrician]

Rearrange your equations so that coefficients of I1 and I2 are together like this:

(5-j2)*I1 + (-3)*I2 = 30
(-5)*I1 + (3+j8)*I2 = 0

Now you can use a standard method to solve them but with complex arithmetic: http://www.mathportal.org/calculators/system-of-equations-solver/system-2x2.php

Will your exam be a take home? If so, you can find solvers on the internet to do the job; search for "simultaneous complex linear equations calculator". If you will be solving systems like this at school, you should get an app for your laptop or get a calculator that can solve simultaneous complex equations.

 

[whatphysics]

Rearrange your equations so that coefficients of I1 and I2 are together like this:

(5-j2)*I1 + (-3)*I2 = 30
(-5)*I1 + (3+j8)*I2 = 0

Now you can use a standard method to solve them but with complex arithmetic: http://www.mathportal.org/calculators/system-of-equations-solver/system-2x2.php

Will your exam be a take home? If so, you can find solvers on the internet to do the job; search for "simultaneous complex linear equations calculator". If you will be solving systems like this at school, you should get an app for your laptop or get a calculator that can solve simultaneous complex equations.

No unfortunately it isn't a take home exam, I have a Texas instrument Graphic Calculator but I don't think it can solve complex simultaneous equations.

But thanks for the great help!

 

[whatphysics]

There are lots of ways to do this sort of problem ...
For complicated meshes, you may find it easier to convert to complex impedences and use a+jb type notation.
So 20∠0 would be just 20+0j, 20∠π/2 would be 0+20j (j=√-1). Then you can solve the simultaneous equations normally.

For simple problems you can usually just add the phasors like vectors.

I will try it again using your method. Thanks for the help!

 

[The Electrician]

No unfortunately it isn't a take home exam, I have a Texas instrument Graphic Calculator but I don't think it can solve complex simultaneous equations.

But thanks for the great help!

What model is your TI calculator?

 

[Hesch]

In "the good old days" FORTRAN implicitly knew about complex numbers.

So if you can make a program that can solve simultaneous equations with real numbers, you just declare these real numbers as complex numbers, and FORTRAN will do the job. All calculations ( addition, division, etc. ) will be done with complex numbers.

 

[whatphysics]

What model is your TI calculator?

TI-84 Plus Pocket SE

 

[The Electrician]

It might be worth your while to get a calculator that can do complex arithmetic. The TI-86 can do complex arithmetic, including matrices with complex arithmetic.

I see them for sale on eBay from $20 to $35.

 

[Babadag]

I, usually, use the excel complex system.
However, at first you have to rearrange the equation as The Electrician said.
a*I1+b*I2=V1 where a=5-j2; b=-3+j0 ;c=-5+j0; d=3+j8; V1=30+j0; V2=0
c*I1+d*I2=V2
1) define a,b,c,d,V1,V2
2) put a=COMPLEX(Re,Im) where Re=5 and Im=-2 in your case.
Do the same with b,c, d,V1 and V2.
3) define DetGen and put IMSUB(IMPRODUCT(a,d),IMPRODUCT(b,c))
4) define DetI1 and set IMSUB(IMPRODUCT(V1,d),IMPRODUCT(V2,b))
5) define DetI2 and put IMSUB(IMPRODUCT(V2,a),IMPRODUCT(V1,c))
6) I1=IMDIV(DetI1,DetGen); I2=IMDIV(DetI2,DetGen)