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Math Help - How to Sketch The following Complex Eqn.

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    How to Sketch The following Complex Eqn.

    pi/4 < Arg[z-(1-i)] < 3pi /4
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    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by saykhong View Post
    pi/4 < Arg[z-(1-i)] < 3pi /4

    Sketch

    \pi/4<\textrm{Arg}\;(w)<3\pi/4

    and interpret geometrically the difference

    w=z-(1-i)
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  3. #3
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    Quote Originally Posted by saykhong View Post
    pi/4 < Arg[z-(1-i)] < 3pi /4
    Note that geometrically Arg(z - z_1) = \theta defines a ray with terminus at z = z1 (this point is not included however) and in the direction (anti-clockwise) of \theta relative to a line parallel to the real axis passing through the terminus.
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