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Math Help - Rewriting imaginary number expression

  1. #1
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    Question Rewriting imaginary number expression

    Write the expression (square root of 12) * (square root of -4) / (square root of 3) in the form a+bi, where a and b are real numbers.
    Thanks for any help!
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  2. #2
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    Quote Originally Posted by live_laugh_luv27 View Post
    Write the expression (square root of 12) * (square root of -4) / (square root of 3) in the form a+bi, where a and b are real numbers.
    Thanks for any help!
     \frac{\sqrt{12}\times \sqrt{-4}}{\sqrt{3}}

     = \frac{\sqrt{12}\times \sqrt{-1 \times 4}}{\sqrt{3}}

     = \frac{\sqrt{12} \times \sqrt{-1} \times \sqrt{4}}{\sqrt{3}}

     = \frac{\sqrt{12} \times i \times 2}{\sqrt{3}}

     = 2i \times  \frac{\sqrt{12}}{\sqrt{3}}

     = 2i \times \sqrt{\frac{12}{3}}

     = 2i \times \sqrt{4}

     = 2i \times 2

     = 4i

     = 0+4i
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  3. #3
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    Thanks!
    What if 12 was negative, how would the problem change??
    Thanks again for your help.
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  4. #4
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    Quote Originally Posted by live_laugh_luv27 View Post
    Thanks!
    What if 12 was negative, how would the problem change??
    Thanks again for your help.
    If 12 was negative then you would do the exact same thing as I did with the -4.

     \sqrt{-12} = \sqrt{12 \times -1}

      = \sqrt{12} \times \sqrt{-1}

      = \sqrt{12} \times i

      = i\sqrt{12}

    In general:

     \sqrt{-a} = i\sqrt{a} .
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