Simultaneous equation with Complex Numbersby Jake2954 Tags: complex, equation, numbers, simultaneous 

#1
Jul2511, 06:18 AM

P: 4

Solve the following simultaneous equations for the complex variables i1 and i2.
2= (3j)_{i1}  (5j2)_{i2}………………(1) 12 = (2+j)_{i1} + (1+j6)_{i2}………………(2) Not sure how to attempt this question please can you help. Thanking you in advance Jake 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 



#2
Jul2511, 07:17 AM

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P: 26,167

Hi Jake! Welcome to PF!
Solve it the same way you would for real simultaneous equations (and use eg 1/(3j) = (3+j)/(3^{2}j^{2})) 



#3
Jul2511, 08:39 AM

P: 4

tt Please excuse my ignorance but I am learning out of a book and need a push in the right direction. Is it possible to show me step by step the correct approach as my head is spinning.




#4
Jul2511, 08:42 AM

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P: 26,167

Simultaneous equation with Complex NumbersShow us how you would solve this if all the coefficients were real. 



#5
Jul2511, 09:02 AM

P: 4

Well the approach I would use is to make either i1 or i2 equal on line 1 + 2 by multiplying by the value of the opposite lines. Lets call them now line 3 + 4. Then I would subtract 4 from 3. This would leave only 1 unknown.




#6
Jul2511, 10:22 AM

P: 4

Still don't understand can anyone else help?




#7
Jul2511, 10:36 AM

P: 3,015

It's a linear system of 2 equations with two variables. You can use the method of determinants (Cramer's rule). One determinant is:
[tex] \Delta = \left\begin{array}{cc} 3  j & 5  2 j \\ 2 + j & 1 + 6 j \end{array}\right = (3  j)(1 + 6 j)  (2 + j)(5  2 j) = 3 + 18 j  j  6 j^2  10 + 4 j  5 j + 2 j^2 = 3 + 16 j [/tex] 


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