[GLOSSARY] arg

[briarsychung]

As said by Andrew Hu on Facebook:

also would like to add that Arg(page 16, question 21) should have a definition in the glossary

[anematode]

Arg is hard to define well without entering into a discussion of multivalued functions. In particular, arg z maps to the set of all coterminal angles pointing to z if z ≠ 0, otherwise it is undefined. For example, arg (i) = { ..., -3 pi / 2, pi / 2, 5 pi / 2, ... }. I guess you could say that arg maps C -> P(C), where P denotes the power set and C is the set of complex numbers. (Ah, I wish Fonts worked on computers too.)

[anematode]

I think the definition should just be:

Arg(z) is the angle which z forms in the complex plane with (0, 0) and the positive real axis, so that Arg(z) is always in the interval (-pi, pi].

This follows the convention that Arg is the principal value, while arg is the multivalued function. Disturbing!

[ky28059]

Almost a year old... what happened to arg?

[briarsychung]

Hey, it's been almost two years now, any updates?? Re-assigning this to the right people.

[ytchang05]

@anematode and I are currently discussing plans to actually have a comprehensive glossary / review guide for students, so this will likely be added there if we are successful.