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Complex numbers help

  1. Jul 6, 2014 #1

    kay

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    We know that i^3 is -i .
    But I am getting confused, because I thought that i can be written as √(-1) and i^3 = √(-1) × √(-1) × √(-1) = √(-1 × -1 × -1) = √( (-1)^2 × -1) = √(1× -1) = √(-1) = i
    ( and not -i ).
    Please help.:rolleyes:
    Sorry I couldn't use superscript because I was using my phone.
     
  2. jcsd
  3. Jul 6, 2014 #2

    micromass

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  4. Jul 6, 2014 #3
    i definitely is not \sqrt{-1}. If you like (abuse of notation)
    \sqrt{-1} = \pm i
    Using (this not correct notation) \sqrt{-1}^3 = \pm i. Much better is of course
    i^3 = (i*i)*i = -1*i = -i
     
  5. Jul 6, 2014 #4

    kay

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  6. Jul 6, 2014 #5

    kay

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    I didn't understand anything. :|
     
  7. Jul 7, 2014 #6

    The link given by micromass has everything you need to know and you don't need to know Euler's Formula to understand what he meant. I suggest read (not skim) the link provided by micromass.
     
  8. Jul 9, 2014 #7
    When you got to this point: $$\sqrt{-1}\cdot\sqrt{-1}\cdot\sqrt{-1}=\sqrt{(-1)\cdot(-1)\cdot(-1)},$$ you made a mistake since [itex]\sqrt{a}\sqrt{b}=\sqrt{ab}[/itex] isn't true when [itex]a,b\lt0[/itex].
     
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