In a book I am studying, while solving something, it does the following thing:
From here $$ e^{-iωτ}=\frac{1}{2}-iω$$
it goes here
$$ τ=\frac{-arg(1/2-iω)}{ω} $$
However I don't get how this happened. I looked up properties to do it my self, but I can't find it. Can anybody tell me what properties where used to do this?
P.S. I hope this question is valid for this Q&A. I have spent 2 hours trying to solve this, something that I think is really easy.
The answer was from @TrevorNorton comment. I am just writing it down for completion reasons.
The property used is ( based on the definitions of $arg()$ and $e^{θi}$ ): $$ arg(e^{θi})=θ $$
So by applying $arg()$ on both sides, we can get the exponential out.