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Homework Help: Sign of u and v in a complex variable

  1. Feb 20, 2012 #1
    1. The problem statement, all variables and given/known data
    if z=x+iy and sqrt(z) = u+iv

    u=±(1/√2)*√(x+√(x^2+y^2 ))
    v=±(1/√2)*√(-x+√(x^2+y^2 ))
    How must the signs on these result be chosen?

    2. The attempt at a solution
    I wondered if it was something to do with ensuring √(z) was always positive, but then ruled this out as it is a complex function. I don't really know where to do with this one! Thanks for your help
  2. jcsd
  3. Feb 20, 2012 #2


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    Hi Fixxxer125! :smile:
    Do the obvious …

    square the second equation: x + iy = z = (u + iv)2,

    then equate real and imaginary parts (separately). :wink:
  4. Feb 20, 2012 #3
    Ah brilliant, thanks!!
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