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Thread: complex number algebra

  1. #1
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    complex number algebra

    $\displaystyle -2 + \frac{\sqrt{-100}}{2} $


    the correct answer is $\displaystyle -1 + 5i $

    here's my work out;

    $\displaystyle -1 + {\sqrt{-50} $ =
    $\displaystyle -1 + \sqrt{50} \times \sqrt{-1} $ =

    $\displaystyle -1 + \sqrt{25} \times \sqrt{2} i $

    $\displaystyle -1 + 5\sqrt{2}i $

    Can someone please show me where I have gone wrong? Thank you.
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  2. #2
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    Re: complex number algebra

    Quote Originally Posted by Tweety View Post
    $\displaystyle -2 + \frac{\sqrt{-100}}{2} $


    the correct answer is $\displaystyle -1 + 5i $

    here's my work out;

    $\displaystyle -1 + {\sqrt{-50} $ =
    $\displaystyle -1 + \sqrt{50} \times \sqrt{-1} $ =

    $\displaystyle -1 + \sqrt{25} \times \sqrt{2} i $

    $\displaystyle -1 + 5\sqrt{2}i $

    Can someone please show me where I have gone wrong? Thank you.
    $\displaystyle \frac{\sqrt{-100}}{2} \ne \sqrt{-50}$


    $\displaystyle \frac{\sqrt{-100}}{2} = \frac{\sqrt{100} \cdot \sqrt{-1}}{2} = \frac{10i}{2} = 5i$
    Thanks from Tweety
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