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anonymous

  • 5 years ago

Ok, I need help figuring out, (-7 + sqrt-5) ^2. I know it's re-written as (-7 + sqrt -5) (-7 + sqrt -5). Do I use FOIL to figure this out?

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  1. KingGeorge
    • 5 years ago
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    FOIL would be an excellent strategy in this case.

  2. anonymous
    • 5 years ago
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    Yes, but rewrite it. sqrt -5 means imaginary..

  3. anonymous
    • 5 years ago
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    |dw:1327303757412:dw|

  4. anonymous
    • 5 years ago
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    how do I rewrite it? I think that's the part that's stumping me

  5. anonymous
    • 5 years ago
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    oh wait, Cinar already did. Thanks! so sqrt -5 equals sq root 5i?

  6. KingGeorge
    • 5 years ago
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    The equation you have is the following correct?\[(-7 + \sqrt{-5})^2\]

  7. anonymous
    • 5 years ago
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    |dw:1327303914040:dw|

  8. anonymous
    • 5 years ago
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    @kinggeorge: Yes, that is correct! how did you get the square root symbo??

  9. KingGeorge
    • 5 years ago
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    If you go into the equation editor on the bottom left of the comment box. For example, you can type "sqrt{-5}" without the quotes to get \[\sqrt{-5}\]It takes some getting used to, but is very clear. Moving on, since that is the equation, cinar's solution is correct.

  10. anonymous
    • 5 years ago
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    I know it's the imaginary units that are throwing me off

  11. KingGeorge
    • 5 years ago
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    As for imaginary units, the square root of negative one is defined as the letter i. Or, \[\begin{matrix} \sqrt{-1} = i \\ i^2 = -1 \end{matrix}\]So if you have a radical such as \[\sqrt{-20}\] you can simplify and solve like so\[\sqrt{-20} = \sqrt{(-1) \cdot 4 \cdot 5} = \sqrt{-1} \cdot \sqrt{4} \cdot \sqrt{5} = 2i \sqrt{5}\]

  12. anonymous
    • 5 years ago
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    wow, this is great!! thank you so much. It's making a lot more sense to me now!

  13. KingGeorge
    • 5 years ago
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    you're very welcome

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