# Writing mod-arg form as $r\operatorname{cis}(\theta)$ rather than $r(\cos\theta + i\sin\theta)$

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.

• en.wikipedia.org/wiki/Cis_(mathematics) – user223391 Jan 15 '17 at 20:37
• It's just their convention. Some texts use that (and so do I sometimes). It's also shorthand for $r e^{i\theta}$. You're okay. – Sean Roberson Jan 15 '17 at 20:38
• Whatever what you want – user223391 Jan 15 '17 at 20:40
• $cis(t)$ is useless notation, because it gets replaced by $e^{it}$ immediately. I recommend getting used to the exponential form. – Kaynex Jan 15 '17 at 20:41
• I think "cis" is teddy-bear for beginners. I guess most people will know what you mean when you write it, but when doing any kind of calculation, $e^{it}$ works better. – B. Goddard Jan 15 '17 at 20:43

## 1 Answer

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.