Imaginary Number Simplification

[jonboy]

What is wrong with my work?

The problem is:\(\displaystyle \L \;\frac{14\,-\,2i}{3\,+\,i}\)

\(\displaystyle \L \;\frac{14\,-\,2i}{3\,+\,i}\,\cdot\,\frac{3\,-\,i}{3\,-\,i}\,=\,\frac{42\,-\,14i\,-\,6i\,+\,2{i}^2}{9\,-\,{i}^2\)

\(\displaystyle \L \;\frac{2{i}^2\,-\,20i\,+\,42}{9\,-\,{i}^2\)

\(\displaystyle \L \;\frac{2(\,-\,1)\,-\,20i\,+\,42}{9\,-\,(-1)}\)

\(\displaystyle \L \;\frac{40\,-\,20i}{10}\,=\,4\,-\,2i\)

 

[galactus]

Looks good, jonboy.

 

[jonboy]

Looks good, jonboy.

Some program I used to check my work gave me a different answer. Oh well. BTW congrats at getting a mod job!

 

[galactus]

What was your other answer from the program:

\(\displaystyle \L\\2\sqrt{5}e^{-itan^{-1}(1/2)}\)?.