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Math Help - 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 tan=\frac{4}{4}=1
    2. then it saids that the arg(z)=\frac{\pi}{4}


    -my concern is, how did it get 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 tan=\frac{4}{4}=1
    2. then it saids that the arg(z)=\frac{\pi}{4}


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

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

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

    \tan{\theta} = 1

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

    \theta = 45^\circ.


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

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

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


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