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Homework Help: Purely Real Proof

  1. Dec 1, 2017 #1
    1. The problem statement, all variables and given/known data
    Find all possible values of ##k## that make ##u = \frac{k+4i}{1+ki}## a purely real number.

    2. Relevant equations


    3. The attempt at a solution
    I calculated the complex conjugate which was ##\frac{5k}{k^2+1} + \frac{4-k^2}{k^2+1}i##. So to prove this do I just solve ##\frac{4-k^2}{k^2+1}## = 0 for ##k##???
    In this case ##k = \pm 2##. Thanks.
     
  2. jcsd
  3. Dec 1, 2017 #2

    PeroK

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    Did you try setting ##k= \pm 2## in the original number to see whether you get a real number?

    Did you mean you multiplied the denominator and numerator by the conjugate of the numerator?
     
  4. Dec 1, 2017 #3
    Yes to the first and yes to the second (conjugate of the denominator though) and it looks all good!!!
     
  5. Dec 1, 2017 #4

    PeroK

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    It does look good!
     
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