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Thread: Complex numbers

  1. #1
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    Complex numbers

    I do not know how to solve the following:

    Write without using absolute value symbols |3i\2-i|. I have been working diligently on the solution, but do not want to show the work I have done so far because I have not mastered LaTex. I went to LaTex, looked up the division sign, and LaTex appeared to instruct me to type \div, but I did not get any results. Perhaps a few pointers on using LaTex, even if it is to direct me to a tutorial
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  2. #2
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    Re: Complex numbers

    Quote Originally Posted by retro View Post
    Write without using absolute value symbols |3i\2-i|.
    I assume that the problem is: $\left|\dfrac{3\bf{i}}{2-\bf{i}}\right|$

    $\dfrac{3\bf{i}}{2-\bf{i}}=\dfrac{(3\bf{i})(2+\bf{i})}{5}=\dfrac{-3+6\bf{i}}{5}$

    Can you finish?

    BTW if you use reply with quote you will see code.
    Last edited by Plato; Aug 27th 2018 at 01:51 PM.
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  3. #3
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    Re: Complex numbers

    Quote Originally Posted by retro View Post
    Write without using absolute value symbols |3i\2-i|.
    I would use the definition directly: $\displaystyle |u| = \sqrt{u^* u}$ :
    $\displaystyle \left | \frac{3i}{2 - i} \right | = \sqrt{ \left ( \frac{3i}{2 - i} \right ) ^* \cdot \left ( \frac{3i}{2 - i} \right ) }$

    $\displaystyle = \sqrt{ \left ( \frac{-3i}{2 + i} \right ) \cdot \left ( \frac{3i}{2 - i} \right ) }$

    $\displaystyle = \sqrt{ \frac{-3i \cdot 3i}{(2 + i)(2 - i)} }$

    and simplify from there.

    -Dan
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