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Thread: 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."



    &

    $\displaystyle x^4 = 256$

    $\displaystyle (x^2)^2 = 256$

    $\displaystyle x^2 = \pm 16$.

    Case 1: $\displaystyle x^2 = 16$

    $\displaystyle x = \pm 4$.

    Case 2: $\displaystyle x^2 = -16$

    $\displaystyle x = \pm 4i$.


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