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Math Help - simple complex conjugates question

  1. #1
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    simple complex conjugates question

    show that :
    |(2\overline{z}+5)(\sqrt{2}-i)|=\sqrt{3}|2z+5|

    so for I have:

    = |(2\overline{z}+5)|\times |(\sqrt{2}-i)|

    = |(2z+5)| \times |(\overline{\sqrt{2}+i})|

    now what I don't understand is how {\color{blue} |(\overline{\sqrt{2}-i})| = |(\overline{\sqrt{2+1}})|} = |\sqrt{3}| = \sqrt{3}
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lllll View Post
    show that :
    |(2\overline{z}+5)(\sqrt{2}-i)|=\sqrt{3}|2z+5|

    so for I have:

    = |(2\overline{z}+5)|\times |(\sqrt{2}-i)|

    = |(2z+5)| \times |(\overline{\sqrt{2}+i})|

    now what I don't understand is how {\color{blue} |(\overline{\sqrt{2}-i})| = |(\overline{\sqrt{2+1}})|} = |\sqrt{3}| = \sqrt{3}
    what you wrote is not true. the final answer is, though.

    recall, |x + iy| = \sqrt{x^2 + y^2}

    so, |\overline{\sqrt{2} - i}| = |\sqrt{2} + i| = \sqrt{(\sqrt{2})^2 + 1^2} = \sqrt{3}
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  3. #3
    Moo
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    Hello,

    The real equality is \left|\overline{z}\right|=\left|z\right|
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