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Math Help - Clarification

  1. #1
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    Clarification

    How should I interpret the difference between f^2(t) and |f(t)|^2? I don't see how they are different, but an application that I'm studying indicates that they are uniquely different. Don't both notatations indicate a squaring of the function?
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  2. #2
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    Quote Originally Posted by kaiser0792 View Post
    Don't both notatations indicate a squaring of the function?
    One squares the function, the other squares the absolute value of the function.
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  3. #3
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    Considering f(x) = -3x, f^2(x) = (-3x)^2 = 9x^2 and |-3x|^2 also equals 9x^2. How are the functions different?
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  4. #4
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    They are not different. But before they were squared they were.
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  5. #5
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    If f is a real valued function then there is no difference between |f(x)|^2 and f^2(x). For real numbers, absolute value can be defined as |x|= \sqrt{x^2} so that |x|^2= x^2.

    If f is complex valued, there is a difference: If f(x)= ix, then |f(x)|= |x| so |f(x)|^2= |x|^2, while (f(x))^2= (ix)^2= -x^2.
    Last edited by HallsofIvy; August 21st 2010 at 02:58 AM.
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  6. #6
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    Thank You
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