Simultaneous equation with Complex Numbers

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Homework Help Overview

The discussion revolves around solving a set of simultaneous equations involving complex variables i1 and i2. The equations are presented in a linear format, similar to real number systems, but include complex coefficients.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various methods for solving the equations, including traditional approaches used for real numbers. Some express confusion and seek step-by-step guidance, while others suggest using techniques like making one variable equal in both equations or applying Cramer's rule.

Discussion Status

The conversation is ongoing, with participants exploring different methods and expressing varying levels of understanding. Some have offered guidance on potential approaches, while others continue to seek clarity on the problem.

Contextual Notes

There are indications of participants feeling overwhelmed and requesting more structured help, which suggests a need for foundational understanding of complex number operations in the context of simultaneous equations.

Jake2954
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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
 
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Welcome to PF!

Hi Jake! Welcome to PF! :smile:

Solve it the same way you would for real simultaneous equations :wink:

(and use eg 1/(3-j) = (3+j)/(32-j2))
 
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.
 
Jake2954 said:
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. :redface:

Show us how you would solve this if all the coefficients were real. :smile:
 
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.
 
Still don't understand can anyone else help?
 
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}<br /> 3 - j & 5 - 2 j \\<br /> <br /> 2 + j & 1 + 6 j<br /> \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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