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Math Help - complex number

  1. #1
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    Question complex number

    Hello friends,
    cant find the root here!
    : Find the sixth roots of (12+5i)
    Thanks,
    Harshal
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by harshal54321 View Post
    Hello friends,
    cant find the root here!
    : Find the sixth roots of (12+5i)
    Thanks,
    Harshal
    convert the number to polar form:

    12 + 5i = 13 e^(i [arctan(5/12) + 2 pi N]), N=0, +/-1. +/-2, ..

    then the sixth roots are:

    (12 + 5i)^(1/6) = (13)^(1/6) e^(i [arctan(5/12) + 2 pi N]/6), N=0, +/-1. +/- 2, ..

    Which give distinct values for N= 0, 1, 2, 3, 4, 5.

    RonL
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  3. #3
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    Hello, Harshal!

    I assume you're familiar with DeMoivre's Theorem . . .


    Find the sixth roots of (12 + 5i)

    Convert to polar form: .12 + 5i .= .13(cosθ + i·sinθ), .where θ = arctan(5/12) .*

    Then: .(12 + 5y)^
    (1/6) . = . 13^(1/6) (cos[θ + 2kπ)/6] + i·sin[(θ + 2kπ)/6])

    . . Evaluate for k = 0, 1, 2, 3, 4, 5


    *
    Edit: corrected my typo.
    . . . .Thanks for pointing it out, Captain.
    Last edited by Soroban; April 4th 2007 at 10:50 AM.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Soroban View Post
    Hello, Harshal!

    I assume you're familiar with DeMoivre's Theorem . . .


    Convert to polar form: .12 + 5i .= .13(cosθ + i·sinθ), .where θ = arctan(5/13)


    cos(theta)=12/13, sin(theta)=5/13, so tan(theta)=5/12

    RonL
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