1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find the real solutions

  1. Apr 12, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the real solutions of

    [itex] \left( 4+2\,i \right) x+ \left( 5-3\,i \right) y=13+i[/itex]



    3. The attempt at a solution

    4x + 2xi + 5y - 3yi = 13 + i

    4x + 5y - 13 + i(2x -3y - 1) = 0

    I am not really sure if my method is correct here for starters.

    Would I then only consider the real part and solve that?
     
  2. jcsd
  3. Apr 12, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The above is correct.

    No. you are looking for the real solutions for x and y, which make the complex equation true.

    In order for a complex equation to be true, the real part of the right side must equal the real part of the left side AND the imaginary part of the right side must equal the imaginary part of the left side
     
  4. Apr 12, 2012 #3
    I'm not entirely sure what you mean, but I think

    4x + 5y = 13 and 2x -3y = 1 ?

    So it's just a simultaneous equation, and solving for x and y gives us real solutions. Is that it?
     
  5. Apr 12, 2012 #4
    Anyone know if this is right?
     
  6. Apr 12, 2012 #5

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    This is correct.

    From your equation:
    4x + 5y - 13 + i(2x -3y - 1) = 0 :​

    Equating the real parts gives:
    4x + 5y - 13 = 0 .​

    Equating the imaginary parts gives:
    2x -3y - 1 = 0 .​

    That's what I mean.
     
  7. Apr 12, 2012 #6
    Damn...thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find the real solutions
  1. Finding a solution (Replies: 5)

  2. Find the solution? (Replies: 13)

  3. Real solutions (Replies: 25)

Loading...