Solving systems of equations with complex numbers

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Discussion Overview

The discussion revolves around solving systems of linear equations that include complex numbers. Participants explore methods for handling these equations, particularly focusing on whether to separate real and imaginary components or to treat them similarly to real coefficients.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants inquire about methods for solving systems of linear equations with complex numbers, suggesting a need for a clear overview.
  • One participant proposes splitting the equations into real and imaginary parts to solve them as separate real systems.
  • Another participant expresses interest in more detailed guidance on the proposed method of separating parts.
  • In contrast, a different participant asserts that linear equations with complex coefficients can be solved in the same way as those with real coefficients, suggesting that separation is unnecessary.

Areas of Agreement / Disagreement

There is no consensus on the best approach to solving these systems, as participants present competing views on whether to separate real and imaginary parts or to treat the equations as they are.

Contextual Notes

Participants have not fully explored the implications of their proposed methods, and there may be assumptions regarding the familiarity with complex numbers and linear algebra that are not explicitly stated.

juicev85
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I can easily solve systems of equations with no complex numbers, could somebody give a short overview of the easiest way to do this by hand.

thanks
 
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juicev85 said:
I can easily solve systems of equations with no complex numbers, could somebody give a short overview of the easiest way to do this by hand.

thanks

I'm guessing from your statement about easily solving that you mean linear systems. In that case, you can split the real and imaginary parts apart and get two separate sets of equations each of which can be solved (as real systems).
 
yes, i need to be able to solve a system of linear equations which include complex numbers. The method you described sounds perfect, is there any way I could get a little more detail?
 
juicev85 said:
yes, i need to be able to solve a system of linear equations which include complex numbers. The method you described sounds perfect, is there any way I could get a little more detail?

Not to my knowledge. I can't figure out what more you might want.
 
Linear equations with complex coefficients can be solved in precisely the same manner as linear equations with real coefficients.
There is no need to split up in real&complex parts.
 

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