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Thread: Determine the sq root of complex number

  1. #1
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    Determine the sq root of complex number

    Question : Determine the sq root of $\displaystyle (3+4i) , \ \ i=\sqrt{-1}$
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    Super Member bigwave's Avatar
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    2 answers

    Quote Originally Posted by zorro View Post
    Question : Determine the sq root of $\displaystyle (3+4i) , \ \ i=\sqrt{-1}$
    this is the same as

    $\displaystyle
    4 + 4i - 1
    $
    which factors to

    $\displaystyle
    (2+i)(2+i)$

    or $\displaystyle (2+i)^2 $

    which $\displaystyle \sqrt{(2+i)^2} = \pm(2+i )$
    Last edited by bigwave; Dec 28th 2009 at 08:18 PM. Reason: wording
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  3. #3
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    Quote Originally Posted by zorro View Post
    Question : Determine the sq root of $\displaystyle (3+4i) , \ \ i=\sqrt{-1}$
    zorro, Do you ever try to do any of the many problems that you post?
    I have not seen any evidence of your work.
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  4. #4
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    But how should i find the amplitute $\displaystyle \theta$ = $\displaystyle tan^{-1} \left( \frac{y}{x} \right)$ = $\displaystyle tan^{-1} \left( \frac{1}{2} \right)$= ?
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  5. #5
    Super Member bigwave's Avatar
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    ok latex error went away

    Amplitude is the magnitude of change in an oscillating variable
    Last edited by bigwave; Dec 28th 2009 at 01:02 PM. Reason: wording
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  6. #6
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    No i want to know what would th amplitute be .........there is no problem with the latex
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    Member Abu-Khalil's Avatar
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    $\displaystyle \sqrt{\left(3+4i\right)}=\sqrt{5e^{i\theta+2\pi}}= \sqrt{5}e^{i\frac{\theta}{2}+\pi},\theta=\arctan\l eft(\frac{3}{4}\right).$
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  8. #8
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    i know that mite i want ot know the value of $\displaystyle \theta$ , i need to find the cos and sin value with it ......
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    Member Abu-Khalil's Avatar
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    You have a triangle rectangle which sides are $\displaystyle 3$ and $\displaystyle 4$. Hipotenuse?
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    Quote Originally Posted by Abu-Khalil View Post
    You have a triangle rectangle which sides are $\displaystyle 3$ and $\displaystyle 4$. Hipotenuse?
    i am not getting it mite ...........the reason i am not getting is because i need the value of $\displaystyle \theta$..............and ur giving me clues which i can get it ..........
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  11. #11
    Member Abu-Khalil's Avatar
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    Quote Originally Posted by zorro View Post
    i am not getting it mite ...........the reason i am not getting is because i need the value of $\displaystyle \theta$..............and ur giving me clues which i can get it ..........
    You don't need the value of $\displaystyle \theta=\arctan\left(\frac{3}{4}\right)$, 'cause that means $\displaystyle \cos\theta=\frac{4}{5},\sin\theta=\frac{3}{5}$.
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  12. #12
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    No u are not getting it i want to express this in polar form ........
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    MHF Contributor Also sprach Zarathustra's Avatar
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    3+4i=5(cos(38.86...+2pi*k)* + isin(36.86...+2pi*k)*)=5cis(36.86... +2pi*k)*

    square root of above can be calculate with de Moivre formula.
    De Moivre's formula - Wikipedia, the free encyclopedia
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  14. #14
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    Quote Originally Posted by bigwave View Post

    this is the same as

    $\displaystyle
    4 + 4i - 1
    $
    which factors to

    $\displaystyle
    (2+i)(2+i)$

    or $\displaystyle (2+i)^2 $

    which $\displaystyle \sqrt{(2+i)^2} = 2+i $
    Actually it's $\displaystyle 2 + i$ or $\displaystyle -(2 + i)$.
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  15. #15
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    could anybody tell me what is the polar form of this equation ............
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