I'm studying in-depth complex numbers and analysis and when I'm working through certain theory, I like to refer to as many textbooks as possible.
I've always known to write mod-arg form as $r(\cos\theta + i\sin\theta)$
However, this book by J. Coroneos writes mod-arg form simplistically as $r\operatorname{cis}\theta$. In the other 7 textbooks I have referred to, I haven't come across this.
Is this is universally accepted? If I use this, will I be technically wrong or is this dude just simplifying things to make things easier.
It's somewhat standard, but mathematicians generally prefer writing $e^{i\theta}$ to writing $\operatorname{cis}\theta.$
The "$\operatorname{cis}$" notation is useful when you want to avoid writing it in the form of an exponential function because the fact that $\theta\mapsto\cos\theta+i\sin\theta$ is an exponential function is just what you're trying to prove.