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Homework Help: Help with Complex function

  1. Jan 12, 2013 #1
    Hi, so for a hw problem I have to evaluate these complex functions. The one I am having trouble on is:

    evaluate h(z) = Re(z) / Im(z) where z = (5-2i) / (2 - i)

    The answer is in the back of the book, which says that the solution is 12, however I keep getting -12i for my answer. I just need someone to tell me where am going wrong.

    I first multiply z by (2 + i) / (2 + i) in order to move the imaginary number to the top, which leaves me with (12 + i) / 5, I then take the real part, 12 / 5 , and put it over the imaginary part, i / 5, and simplify this to 12 / i , where I multiply this by i / i , which leaves me with -12i

    The answer is supposed to be 12, so if anyone could shed some light on this that would be great. Thanks everyone
  2. jcsd
  3. Jan 12, 2013 #2


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    The imaginary part of 12/5 + (1/5)i is 1/5.
  4. Jan 12, 2013 #3

    Ray Vickson

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    Re(z) and Im(z) are both REAL, so their ratio must be real as well.
  5. Jan 12, 2013 #4
    Wow that was pretty obvious. I knew I was messing something up, thanks guys
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