Results 1 to 3 of 3

Math Help - Imaginary number proof problem

  1. #1
    Junior Member
    Joined
    Feb 2011
    Posts
    55

    Imaginary number proof problem

    I've just started imaginary numbers.
    I'm trying to derive what the inverse of j is.
    Where j =\sqrt{-1}

    So I did the following:

    \frac{1}{j}=\frac{z}{1}

    Multiplied j by both sides.

     jz=1

    squared both sides

     -z^2 =1

    and by solving I get that z=j

    which is obviously wrong since  j^2 \neq 1

    Any insights on what I'm over looking?
    I derived it another why, but I want to know why this approach isn't working.
    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Quote Originally Posted by elieh View Post
    Multiplied j by both sides  jz=1 squared both sides  -z^2 =1 and by solving I get that z=j
    You should get z=\pm j . Both are solutions of  -z^2 =1 but only z=-j is solution of jz=1. Why?. Because if we square both sides of an equation, can appear solutions that are not in the original one.

    Another example: the only solution of x=2 is 2 and the solutions of x^2=4 are \pm 2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2011
    Posts
    55
    Alright, Thank you!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: June 6th 2011, 07:39 PM
  2. Replies: 4
    Last Post: January 18th 2011, 04:34 PM
  3. Why is (-2)^(-2)^(-2) an imaginary number?
    Posted in the Math Topics Forum
    Replies: 6
    Last Post: August 13th 2010, 02:33 PM
  4. An odd imaginary number problem (a+bi form)
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 31st 2010, 05:21 PM
  5. imaginary number problem
    Posted in the Algebra Forum
    Replies: 6
    Last Post: September 16th 2007, 11:45 AM

Search Tags


/mathhelpforum @mathhelpforum