For the life of me I can't understand my lecturer's working on this.
I have $$\frac{1}{j\omega{L}}$$
Where $\omega=5000$ and $L=0.0001$
He somehow ended up with $$-2j$$
Whereas I simly got $$\frac{1}{2j}or\frac{j^{-1}}{2}$$
Am I not seeing something or do I need to go back to primary school?
$0.0001 \times 5000$ is $0.5$, $j$ is the complex unit, which mathematicians don't like in the denominator, so they mulitply top and bottom by it's complex conjugate. Hence;
\begin{eqnarray} \frac{1}{j \omega L} &=& \frac{1}{0.5j} \\ &=& \frac{-j}{0.5j(-j)} \\ &=& \frac{-j}{0.5(-1)j^{2}} \\ &=& \frac{-j}{0.5(-1)^{2}} \\ &=& \frac{-j}{0.5} \\ &=& -2j. \end{eqnarray}