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Solving a matrix with complex numbers help

  1. Oct 23, 2008 #1
    1. The problem statement, all variables and given/known data
    ive been given this system of equations and told to solve it:
    x+2y+2z=-3
    2x+y+z=0
    x-y-iz=i


    2. Relevant equations
    all elementary row operations


    3. The attempt at a solution
    1 2 2|-3
    2 1 1| 0 row2-row1 then row2 x -1/3
    1-1-i| i

    1 2 2|-3
    0 1 1|-2 row3-row1 then row3+3 x row2
    1-1-i|i

    1 2 2|-3
    0 1 1|-2
    0 0 5-i|-3+i

    at this point im stuck, i know i have to get it in reduced row echelon form, but that 5-i has got me scratching my head, and somehow i know i have to get it to be 1 in order to reduce the other rows.
     
  2. jcsd
  3. Oct 23, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You do exactly what you do with real numbers! Divide both sides by 5-i. If you want to get (-3+i)/(5- i) in "a+ bi" form, try multiplying both numerator and denominator by 5+ i.
     
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