Finding Solutions to Complex Linear Systems

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Discussion Overview

The discussion focuses on finding solutions to a system of complex linear equations involving two variables, z and w. Participants explore methods for solving the system, including matrix representation and algebraic manipulation.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents a system of equations and expresses difficulty in finding a solution, mentioning attempts at expansion and matrix representation.
  • Another participant suggests multiplying the first equation by a specific factor to align the coefficients of z in both equations, followed by subtracting the first equation from the second to solve for w.
  • A different participant reassures that the presence of complex numbers does not change the approach to solving the equations, recommending division by the leading coefficient in the first equation.
  • A later reply indicates that the original poster feels they have made progress in understanding the solution process.

Areas of Agreement / Disagreement

Participants generally agree on the methods to approach the problem, but there is no explicit consensus on the final solution or the best method to use.

Contextual Notes

Some participants' suggestions depend on specific algebraic manipulations that may not be universally applicable without additional context or assumptions about the equations.

Who May Find This Useful

Students and individuals interested in solving complex linear systems, particularly those who may be struggling with similar mathematical concepts.

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Find the solution in C to the following linear system of equations.

(a) (1-i)z + 4w = 2 + 8i
(b) 3z + (1+i)w = 1 + 5i

I tried expanding but that didn't get me anywhere. Then i put it in a matrix, but i didn't know how to go from there. Any suggestions? Thanks.
 
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1.Multiply your first equation with 3/2*(1+i)
You should then have 3z in both equations.
2. Then subtract the first from the second and solve for w.
3) Don't bother to expand brackets until you've solved for w and z
 
Don't be intimidated by the complex numbers. You would solve this problem exactly as you would if there were only real numbers involved.

For instance, in the first equation, the coefficient on z is simply the (single!) number (1 - i). So, if when solving systems of equations, you like to divide through by the leading coefficient, then you would do so, by dividing through by (1 - i).
 
thanks guys...i think i got it...
 

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