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Math Help - Complex inequalities, Please help.

  1. #1
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    Complex inequalities, Please help.

    Hi everyone, this is my first time on this forum, so please bear with me.

    I am currently going over some paper and came across this:

    Let x, y be complex #s and IxI+IyI=1. If a,b are also elements of complex numbers and Ix +/- aI + Iy +/- bI <= 1

    The author claims that if x*y is not 0, then

    I IxI +/- a*(IxI/x)I + I IyI +/- b*(IyI/y)I <=1

    Sorry about this notation, IxI denotes the modulus of x and +/- means + or -. Any help is appreciated. Thanks!
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  2. #2
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    Quote Originally Posted by ChiliNBeans View Post
    Hi everyone, this is my first time on this forum, so please bear with me.

    I am currently going over some paper and came across this:

    Let x, y be complex #s and IxI+IyI=1. If a,b are also elements of complex numbers and Ix +/- aI + Iy +/- bI <= 1

    The author claims that if x*y is not 0, then

    I IxI +/- a*(IxI/x)I + I IyI +/- b*(IyI/y)I <=1

    Sorry about this notation, IxI denotes the modulus of x and +/- means + or -. Any help is appreciated. Thanks!

    Too cumbersome notation. Refer to the help in Latex section of the group.

    Tonio
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