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Math Help - Complex Principal Argument

  1. #1
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    Complex Principal Argument

    Determine the principle value of the argument

    -1-i

    tan( \theta) = -1/-1 = \frac{\pi}{2} but it is negative because it is in the 4th quadrant

    the answer is \frac{-3\pi}{4}

    Principle Argument is simple the argument except between the values of -\pi and \pi

    What did i do wrong?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Fallen186 View Post
    Determine the principle value of the argument

    -1-i

    tan( \theta) = -1/-1 = \frac{\pi}{2} but it is negative because it is in the 4th quadrant

    the answer is \frac{-3\pi}{4}

    Principle Argument is simple the argument except between the values of -\pi and \pi

    What did i do wrong?
    \tan^{-1}\left(\tfrac{-1}{-1}\right)=\frac{\pi}{4}.

    However, \theta is in the fourth quadrant. So it follows that \theta=\frac{\pi}{4}-\pi=-\frac{3\pi}{4}.

    Does this make sense?
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