1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B Imaginary number manipulations

  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?
  2. jcsd
  3. Apr 2, 2016 #2


    User Avatar
    Homework Helper

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


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Imaginary number manipulations
  1. Imaginary Numbers (Replies: 9)

  2. Imaginary Numbers (Replies: 4)

  3. Imaginary Numbers (Replies: 14)