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Complex number question

  1. Feb 8, 2006 #1
    Hi I'm fairly new to complex numbers and was yesterday presented with the following assignment.

    Find [tex]w,z \in \mathbb{C} [/tex]

    [tex]w + (1+i)z = -1[/tex]

    [tex](1-i) - z = 1[/tex]

    Any hints on how to solve these equations?

    Sincerely Yours

  2. jcsd
  3. Feb 8, 2006 #2


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    Homework Helper

    Systems of linear equations with complex numbers can be solved with the same methods used for real systems, perhaps easiest are matrix methods or Cramer's rule.
  4. Feb 8, 2006 #3


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    Homework Helper

    For example--oh, it is easier to do this:

    (1) [tex]w + (1+i)z = -1[/tex]
    (2) [tex](1-i) - z = 1[/tex]

    (2) gives z=-i (by adding z-1 to both sides), substitute this into (1) to get

    [tex]w + (1+i)(-i) = -1[/tex]
    [tex]w + -i+1 = -1[/tex]
    [tex]w = -2+i[/tex]

    so the final answer is z=-i and w=-2+i
  5. Feb 8, 2006 #4


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    Staff Emeritus
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    Gold Member

    You generally solve complex equations the same way you would solve real equations.
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