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Thread: argument of z.

  1. #1
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    argument of z.

    the given example in the book states the argument of z=4+4i.

    1. it has said to use $\displaystyle tan=\frac{4}{4}=1$
    2. then it saids that the $\displaystyle arg(z)=\frac{\pi}{4}$


    -my concern is, how did it get $\displaystyle arg(z)=\frac{\pi}{4}$ ?
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  2. #2
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    Quote Originally Posted by johnsy123 View Post
    the given example in the book states the argument of z=4+4i.

    1. it has said to use $\displaystyle tan=\frac{4}{4}=1$
    2. then it saids that the $\displaystyle arg(z)=\frac{\pi}{4}$


    -my concern is, how did it get $\displaystyle arg(z)=\frac{\pi}{4}$ ?
    It's actually

    $\displaystyle \tan{\theta} = \frac{y}{x}$ (since the angle is in the first quadrant)

    $\displaystyle \tan{\theta} = \frac{4}{4}$

    $\displaystyle \tan{\theta} = 1$

    $\displaystyle \theta = \arctan{1}$ (or $\displaystyle \tan^{-1}{1}$, depending on which notation you use)

    $\displaystyle \theta = 45^\circ$.


    Now since $\displaystyle 360^\circ = 2\pi^C$

    $\displaystyle \frac{360^\circ}{8} = \frac{2\pi^C}{8}$

    $\displaystyle 45^\circ = \frac{\pi}{4}^C$.


    So $\displaystyle \arg{z} = \frac{\pi}{4}^C + 2\pi^Cn$, where $\displaystyle n$ is an integer representing the number of times you have gone around the unit circle.
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