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Math Help - Solutions for imaginary numbers in a+bi

  1. #1
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    Solutions for imaginary numbers in a+bi

    A sample problem is:


    Find all solutions of the equation and express them in the form a + bi.

    x^2-7x+13=0



    I'm supposed to get 2 answers. A positive conjugate and a negative conjugate.


    However when I solve it, I get an odd fraction and the website keeps telling me that this is a wrong answer. And the formatting is right. So I know I'm doing something wrong.


    Could someone tell me how these sort of problems are solved? I know most of the steps, but I'm missing something.



    Thanks.
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  2. #2
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    Quote Originally Posted by DustinP View Post
    A sample problem is:


    Find all solutions of the equation and express them in the form a + bi.

    x^2-7x+13=0



    I'm supposed to get 2 answers. A positive conjugate and a negative conjugate.


    However when I solve it, I get an odd fraction and the website keeps telling me that this is a wrong answer. And the formatting is right. So I know I'm doing something wrong.


    Could someone tell me how these sort of problems are solved? I know most of the steps, but I'm missing something.



    Thanks.
    You can complete the square or use the Quadratic Formula:

    x^2 - 7x + 13 = 0

    x^2 - 7x + \left(-\frac{7}{2}\right)^2 - \left(-\frac{7}{2}\right)^2 + 13 = 0

    \left(x - \frac{7}{2}\right)^2 - \frac{49}{4} + \frac{52}{4} = 0

    \left(x - \frac{7}{2}\right)^2 + \frac{3}{4} = 0

    \left(x - \frac{7}{2}\right)^2 = -\frac{3}{4}

    x - \frac{7}{2} = \pm \sqrt{-\frac{3}{4}}

    x - \frac{7}{2} = \frac{\pm \sqrt{-3}}{\sqrt{4}}

    x - \frac{7}{2} = \frac{\pm \sqrt{3}i}{2}

    x = \frac{7}{2} \pm \frac{\sqrt{3}}{2}i


    So the two solutions are:

    x = \frac{7}{2} + \frac{\sqrt{3}}{2}i and x = \frac{7}{2} - \frac{\sqrt{3}}{2}i.
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  3. #3
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    Quote Originally Posted by DustinP View Post
    A sample problem is:


    Find all solutions of the equation and express them in the form a + bi.

    x^2-7x+13=0



    I'm supposed to get 2 answers. A positive conjugate and a negative conjugate.


    However when I solve it, I get an odd fraction and the website keeps telling me that this is a wrong answer. And the formatting is right. So I know I'm doing something wrong.
    It would have been better if you had shown us what wrong answer you got!


    Could someone tell me how these sort of problems are solved? I know most of the steps, but I'm missing something.



    Thanks.
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  4. #4
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    Ahh. Ok Thanks. I put that answer in and it is right.

    What I was doing (or not doing) was keeping the square root of 3. So I just had 3 over 2. But I see what you did now, I think.

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  5. #5
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    I had:

    x = \frac{7}{2} - \frac{3}{2}i<br />

    x = \frac{7}{2} + \frac{3}{2}i<br />
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  6. #6
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    Quote Originally Posted by DustinP View Post
    Find all solutions of the equation and express them in the form a + bi. x^2-7x+13=0
    x=\frac{7\pm\sqrt{7^2-4(13)}}{2}
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