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!

1 = -1 where is the error

  1. Nov 18, 2005 #1
    I've tried and tried and I cannot find the error in the reasoning below. It's probably something simple and I'll feel like an idiot when someone explains it.
    i = i
    sqrt(-1) = sqrt(-1)
    sqrt(1/-1) = sqrt (-1/1)
    sqrt(1)/sqrt(-1) = sqrt(-1)/sqrt(1)
    sqrt(1) * sqrt(1) = sqrt(-1) * sqrt(-1)
    [sqrt(1)]^2 = [sqrt(-1)]^2
    1 = -1

    Does it have something to do with sqrt(-1/1) = sqrt(-1)/sqrt(1)? Does complex numbers not obey this property?
  2. jcsd
  3. Nov 18, 2005 #2
    doesnt [sqrt(a)]^2 = |a| ? maybe thats just in the reals
    Last edited: Nov 18, 2005
  4. Nov 18, 2005 #3
    [tex]\frac{\sqrt{1}}{\sqrt{-1}}[/tex] pretty much sums up what's wrong with the train of thought. This is a good reason why when you divide a real number by an imaginary number that you must first multiply by the conjugate on the numerator and denominator. I can't nail down a good reason other than that.

    I should note that this inconsitency does not exist if you do the division with sqrt(1) and sqrt(-1) in polar form.
  5. Nov 19, 2005 #4

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    square rooting is 1 to 2, so you need to pick a choice of square root. You've not done so consitently.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook