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Thread: Imaginary number proof problem

  1. #1
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    Imaginary number proof problem

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

    So I did the following:

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

    Multiplied j by both sides.

    $\displaystyle jz=1 $

    squared both sides

    $\displaystyle -z^2 =1 $

    and by solving I get that z=j

    which is obviously wrong since $\displaystyle 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!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by elieh View Post
    Multiplied j by both sides $\displaystyle jz=1 $ squared both sides $\displaystyle -z^2 =1 $ and by solving I get that z=j
    You should get $\displaystyle z=\pm j$ . Both are solutions of $\displaystyle -z^2 =1 $ but only $\displaystyle z=-j$ is solution of $\displaystyle jz=1$. 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 $\displaystyle x=2$ is $\displaystyle 2$ and the solutions of $\displaystyle x^2=4$ are $\displaystyle \pm 2$
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  3. #3
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    Alright, Thank you!
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