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Thread: arg(z)=\frac{\pi}{4}

  1. #1
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    arg(z)=\frac{\pi}{4}

    Describe the set of points z in the complex plane that satisfy $\displaystyle arg(z)=\frac{\pi}{4}$.

    Is this question just asking for $\displaystyle x=\frac{\sqrt{2}}{2}$ and $\displaystyle y=\frac{\sqrt{2}}{2}$?
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  2. #2
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    no, the set is a whole line, not just one point. All complex numbers on the line $\displaystyle r(\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\cdot i)=r e^{i \frac{\pi}{4}}$ for r $\displaystyle \in \mathbb{R}, r>0$.
    See also
    Complex number - Wikipedia, the free encyclopedia
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    Quote Originally Posted by dwsmith View Post
    Describe the set of points z in the complex plane that satisfy $\displaystyle arg(z)=\frac{\pi}{4}$.

    Is this question just asking for $\displaystyle x=\frac{\sqrt{2}}{2}$ and $\displaystyle y=\frac{\sqrt{2}}{2}$?
    It is a ray with terminus at (0, 0) and making an angle of pi/4 with the positive real axis. (0, 0) is not included since Arg(0) is not defined.
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    Which means it is the set $\displaystyle \{a+ bi| a= b, a> 0\}$
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