Simultaneous equation with Complex Numbers

[Jake2954]

Solve the following simultaneous equations for the complex variables i1 and i2.

2= (3-j)_i1 - (5-j2)_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

 

[tiny-tim]

Welcome to PF!

Hi Jake! Welcome to PF!

Solve it the same way you would for real simultaneous equations

(and use eg 1/(3-j) = (3+j)/(3²-j²))

 

[Jake2954]

t-t 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.

 

[tiny-tim]

t-t 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.

Sorry, Jake, this forum doesn't work that way.

Show us how you would solve this if all the coefficients were real. ​

 

[Jake2954]

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. Let's call them now line 3 + 4. Then I would subtract 4 from 3. This would leave only 1 unknown.

 

[Jake2954]

Still don't understand can anyone else help?

 

[Dickfore]

It's a linear system of 2 equations with two variables. You can use the method of determinants (Cramer's rule). One determinant is:

$$\Delta = \left|\begin{array}{cc} 3 - j & 5 - 2 j \\ 2 + j & 1 + 6 j \end{array}\right| = (3 - j)(1 + 6 j) - (2 + j)(5 - 2 j) = 3 + 18 j - j - 6 j^2 - 10 + 4 j - 5 j + 2 j^2 = -3 + 16 j$$