1. ## 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

2. ## Re: Complex numbers

Originally Posted by retro
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.

3. ## Re: Complex numbers

Originally Posted by retro
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