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Homework Help: Polar form and arg(z) problem

  1. Apr 7, 2012 #1
    1. The problem statement, all variables and given/known data

    express the arg(z) and polar form of

    ([itex]1/\sqrt{2}[/itex]) - ([itex]i/\sqrt{2}[/itex])

    2. Relevant equations

    3. The attempt at a solution

    Ok so I did [itex]\sqrt{(1/\sqrt{2})^{2}+(1/\sqrt{2})^{2}}[/itex] = 1

    so tan[itex]^{-1}[/itex](1) = [itex]\pi/4[/itex] so arg(z)=5[itex]\pi[/itex][itex]/4[/itex]

    but they had the answer as [itex]-3\pi/4[/itex]

    Am I wrong or are they because shouldnt the arg(z) lie in the third quad.??
  2. jcsd
  3. Apr 8, 2012 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    A better question for you is why do those numbers represent the same angle
  4. Apr 8, 2012 #3


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    Science Advisor

    Both [itex]5\pi/4[/itex] and [itex]-3\pi/4[/itex] are in the third quadrant.
  5. Apr 8, 2012 #4
    Were they asking for the principal argument? i.e. Arg(z)? Arg(z) is defined to be in the range of [itex](-\pi,\pi][/itex]
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