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Math Help - factorise with i

  1. #1
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    factorise with i

    im stuck on how to factor out the i.

    108+36\sqrt{3i}+12i\sqrt{3i}+36i
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by skystar View Post
    im stuck on how to factor out the i.

    108+36\sqrt{3i}+12i\sqrt{3i}+36i
    Try rewriting the expression. I'll give you a jump start:

    108+36\sqrt{3}\sqrt{i}+12i\sqrt{3}\sqrt{i}+36i.

    My next hint is that \sqrt{i}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i.

    I'm not quite sure that you can indeed factor out an i, but at least you can simplify the expression and get it in the form a+bi. Hope this helped you out a little bit!
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  3. #3
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    Hello, skystar!

    Why do you want to factor out an i ?


    Factor: . 108+36\sqrt{3i}+12i\sqrt{3i}+36i

    We have: . 108 + 36\sqrt{3i} + 36i + 12i\sqrt{3i}

    Factor out 12: . 12\,\bigg[9 + 3\sqrt{3i} + 3i + i\sqrt{3i}\bigg]

    Factor by grouping: . 12\,\bigg[3(3+\sqrt{3i}) + i(3+\sqrt{3i})\bigg]

    . . Therefore: . 12\,(3+\sqrt{3i})\,(3 + i)

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