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Homework Help: Complex Number-how to show it ?

  1. Sep 3, 2004 #1
    Complex Number---how to show it ?

    Given that z = x + yi and
    w = ( z + 8i )/(z - 6) , z not equal to 6 .
    If w is totally imaginary, show that :
    x^2 + y^2 + 2x - 48 = 0

    i understand the question, but the problem i facing is i only be able to show :
    x^2 + y^2 - 6x + 8y = 0
    i think that in order to satisfy what the question ask , i need to find y in term of x, but i cant do it.....i dont sure whether is the question wrong already or my mistake. Any expert there, please help.
  2. jcsd
  3. Sep 3, 2004 #2
    w is totally imaginary <=> Re(w) = 0 <=> ...
  4. Sep 3, 2004 #3

    matt grime

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    Science Advisor
    Homework Helper

    I think there are too many continuations of that ellipsis (well, two), so as an aid, have you been taught how to convert division by a complex number into mulitplication by a complex number (one written as real plus i times imaginary)?

    1/z = z*/(|z|^2)

    now look at the imaginary part

    (for muzza the other posibility i thought of involved the argument which didn't seem useful, though that was only a first impression)
  5. Sep 3, 2004 #4
    If z=0 then w=-4i/3 which is totally imaginary, but -48<>0

    I think the numerator should be (z + 8)
  6. Sep 3, 2004 #5
    yes it should be (z+8)
    simply note that (x+8)(x-6) = x^2+2x-48
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