Complex numbers help

  1. 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. micromass

    micromass 19,677
    Staff Emeritus
    Science Advisor
    Education Advisor

  4. 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. I didn't understand anything. :|
     

  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.
     
    1 person likes this.
  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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