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Complex number question

  1. Jan 27, 2010 #1
    1. The problem statement, all variables and given/known data If [tex]z = \frac{a}{b}[/tex] and [tex]\frac{1}{a + b} = \frac{1}{a} + \frac{1}{b}[/tex], find z.



    2. Relevant equationsI'm pretty sure z is a complex number.



    3. The attempt at a solutionI have no idea where to start. The teacher did nothing like this in class. I tried something that involved combining the fractions on the right hand side and then cross-multiplying with the fraction on the left hand side. I played around with that for a few minutes but it didn't give me anything.
     
  2. jcsd
  3. Jan 27, 2010 #2
    I am confused about what you are asking. z is defined. Are you trying to get z in different terms than above? Or perhaps in cartesian/standard or polar form?
     
  4. Jan 27, 2010 #3
    Keep playing. It works out.
     
  5. Jan 27, 2010 #4

    Dick

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    Homework Helper

    Multiply both sides of your equation by (a+b) and try to reduce the right side to terms that are constants or a/b, or b/a. a/b=z. Doesn't that make b/a=1/z? Write it all in terms of z. Think 'quadratic equation'.
     
  6. Jan 27, 2010 #5
    I think I got it. I substituted zb for a. I combined and cross multiplied again. I ended up with [tex]z = \frac{-1}{2} \pm \frac{i\sqrt{3}}{2}[/tex]

    Now I need to check it...
     
  7. Jan 27, 2010 #6
    It checks! w00t \O/
     
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