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Thread: modulus

  1. #1
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    modulus

    Lets say P and Q are both complex numbers . The modulus of P and Q are 1 and 2 respectively .

    The question is find the modulus for the complex numbers a , b and c with

    $\displaystyle a=p^4$ ,$\displaystyle b=q^2$ , $\displaystyle c=-ip $

    so $\displaystyle |a|=|p|^4 = 1^4 =1 $

    $\displaystyle
    |b|=|q|^2 = 2^2
    $

    Am i right in saying that ???
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by thereddevils View Post
    Lets say P and Q are both complex numbers . The modulus of P and Q are 1 and 2 respectively .

    The question is find the modulus for the complex numbers a , b and c with

    $\displaystyle a=p^4$ ,$\displaystyle b=q^2$ , $\displaystyle c=-ip $

    so $\displaystyle |a|=|p|^4 = 1^4 =1 $

    $\displaystyle
    |b|=|q|^2 = 2^2
    $

    Am i right in saying that ???
    it is right

    for $\displaystyle c=-ip$ suppose that $\displaystyle p=x+iy$ so $\displaystyle \mid p \mid =\sqrt{x^2+y^2}=1$

    $\displaystyle \mid c\mid =\mid -i(x+iy) \mid = \mid -ix+y \mid = \sqrt{(-x)^2+y^2}=\sqrt{x^2+y^2} =1 $ from above
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  3. #3
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    Quote Originally Posted by Amer View Post
    $\displaystyle \mid c\mid =\mid -i(x+iy) \mid = \mid -ix+y \mid = \sqrt{(-x)^2+y^2}=\sqrt{x^2+y^2} =1 $ from above
    Why not just notice that $\displaystyle \left| {wz} \right| = \left| w \right|\left| z \right|\, \Rightarrow \,\left| { - ip} \right| = \left| { - i} \right|\left| p \right| = \left| p \right|$?
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