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B Imaginary number manipulations

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  1. Apr 2, 2016 #1
    I know that this is probably a very commonly asked question with students, but say that we have ##\sqrt{(-1)^2}##. If we performed the innermost operation first, then we have ##\sqrt{(-1)^2} = \sqrt{1} = 1##. However, according to rules for radicals, we can do ##\sqrt{(-1)^2} = (\sqrt{-1})^2 = -1##. Which one of these is the correct way of going about evaluating the expression, and why?
     
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  3. Apr 2, 2016 #2

    Math_QED

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    ##\sqrt{(a)^2}## = |a|
     
  4. Apr 2, 2016 #3

    FactChecker

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    If you are really going to study imaginary and complex numbers, you will find out that roots do not have unique values, but rather they can have several "branches". Notice that (-1)2 = 1. So you could also have a square root, sqrt(), of 1 where sqrt( -12 ) = sqrt( 1) = -1. The standard definition of √ is that it is the "principle branch". But that is just a convention, not a mathematical rule.
     
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