Equations with complex numbers

G

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A and B are two complex numbers that satisfy the following:
(2 + j3)A + (3 - j5)B = (6 + j9)
(1 - j2)A + (4 + j3)B = (7 - j10)
Find A and B.

Do I set up a matrix and solve?
Thanks.
 
If j3 means \(\displaystyle \mbox{j^3}\) where \(\displaystyle \mbox{j = \sqrt{-1}}\), then, yes, that will certainly work, after simplifying the powers of j.

Remember that your solutions can be simplified by multiplying the top and bottom by the complex conjugate of the denominator.
 
No, j3 means 3*j (or i, whatever you like to use).

I don't see how multiplying by complex conjugate will help here.
 
j3 = 3 * j . . . ok. Same deal.

Have you solved the system yet? Multiplying by the conjugate is merely to simplify your >solutions<.
 
I agree a matrix is probably the way to go. It gets messy expanding the products to get the four equations in four unknowns but I can't think of a better way.
I don't understand where Unco found a denominator either.
 
I created an augmented matrix and solved on my graphing calculator and i got
A=4.11288/A-.04561/A
B=.269099/B-.63397/B

Doesn't make any sense..and my calculator is set to rectangular complex format.

Would writing it as this help:

(2 + j3)jx + (3 - j5)jy = (6 + j9)
(1 - j2)jx + (4 + j3)jy = (7 - j10)
 
Why are you using a calculator?

(2 + 3j)A + (3 - 5j)B = (6 + 9j) [1]
(1 - 2j)A + (4 + 3j)B = (7 - 10j) [2]

Multiply [1] by (1 - 2j) and [2] by (2 + 3j), simplify, and subtract the resulting equations to get:

(-6 - 29j)*B = -20 - 4j
 
Ah, good observation Unco.

Ironically, though, my calculator had given me the right answer..
I misinterpreted the matrix my calculator gave me
1=4.11288/A - j*0.04561/A
1=.269099/B - j*0.63397/B

solving, A=4.11-j0.046 and B=.269-j0.634

that's why I use my calculator :)

anyways, thanks a lot for the help!
 
I was probably taking the long way around.
A=u+vj, B=w+xj
Doing the multiplication
(2+3j)(u+vj) etc.
then equating the reals and imaginaries and putting them in a 4x5 matrix to solve for u,v,w & x.
----------------
Gene

PS. That's what I got too. (Finally)
 
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