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Math Help - 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 (3+4i) , \ \ i=\sqrt{-1}
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  2. #2
    Super Member bigwave's Avatar
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    2 answers

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

     <br />
4 + 4i - 1<br />
    which factors to

     <br />
(2+i)(2+i)

    or (2+i)^2

    which \sqrt{(2+i)^2} = \pm(2+i )
    Last edited by bigwave; December 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 (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 \theta = tan^{-1} \left( \frac{y}{x} \right) = 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; December 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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  7. #7
    Member Abu-Khalil's Avatar
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    \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 \theta , i need to find the cos and sin value with it ......
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  9. #9
    Member Abu-Khalil's Avatar
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    You have a triangle rectangle which sides are 3 and 4. Hipotenuse?
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    Quote Originally Posted by Abu-Khalil View Post
    You have a triangle rectangle which sides are 3 and 4. Hipotenuse?
    i am not getting it mite ...........the reason i am not getting is because i need the value of \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 \theta..............and ur giving me clues which i can get it ..........
    You don't need the value of \theta=\arctan\left(\frac{3}{4}\right), 'cause that means \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

     <br />
4 + 4i - 1<br />
    which factors to

     <br />
(2+i)(2+i)

    or (2+i)^2

    which \sqrt{(2+i)^2} = 2+i
    Actually it's 2 + i or -(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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