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Math Help - Principle Argument of a Complex number?

  1. #1
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    Principle Argument of a Complex number?

    Alright all ive got the complex number

    (8)^1/2 - i (24)^1/2.

    So i put Tan theta = root 24 / root 8

    I get theta as Pi/3.

    Is this the principle agrument?
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  2. #2
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    Quote Originally Posted by simpleas123 View Post
    Alright all ive got the complex number
    (8)^1/2 - i (24)^1/2.
    So i put Tan theta = root 24 / root 8
    I get theta as Pi/3.
    Is this the principle agrument?
    No it is not.
    Note that if x>0 then \arg(x+yi)=\arctan\left(\frac{y}{x}\right).
    In this case y=-\sqrt{24} so \left(\frac{-\pi}{3}\right).
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