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Math Help - Complex numbers

  1. #1
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    Complex numbers

    hi all,

    i need help with two problems that read: "solve the equation in the complex number system."



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  2. #2
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    Quote Originally Posted by needleandthread View Post
    hi all,

    i need help with two problems that read: "solve the equation in the complex number system."



    &

    x^4 = 256

    (x^2)^2 = 256

    x^2 = \pm 16.

    Case 1: x^2 = 16

    x = \pm 4.

    Case 2: x^2 = -16

    x = \pm 4i.


    So the four solutions are 4, 4i, -4, -4i.
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  3. #3
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    The second expression, x^3- 343, isn't and equation but I assume you meant x^3= 343. Since the first equation had a simple integer solution, x= 2, the first thing you should do is start cubing integers. You find that 7^3= 343. Then x^3- 7^3= (x- 7)(x^2+ 7x+ 49). x= 7 is one solution and you can find the other two by solving x^2+7x+ 49= 0 with the quadratic formula.
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