Naming of `phase` argument label for `Complex` about swift-numerics HOT 3 CLOSED

phase is certainly more common than angle in this use, and definitely more specific (angle is used in lots of other contexts). For one example, on the wikipedia page for complex numbers, phase appears with exactly this meaning; the closest angle comes is "the angle of the radius Oz with the positive real axis".

I'm open to being convinced, but currently weakly in favor of keeping phase.

from swift-numerics.

phase is certainly more common than angle in this use

I am not convinced of this.

and definitely more specific (angle is used in lots of other contexts).

Nor of this. Phase is also used in lots of other contexts. For example:

Phases of matter in chemistry
Phases of development in biology
Phase space in dynamical systems
Phases of a project in engineering
Phases of the moon in astronomy
etc.

With “angle”, if the context is even vaguely related to math / physics / engineering, there’s only one meaning.

For one example, on the wikipedia page for complex numbers, phase appears with exactly this meaning; the closest angle comes is "the angle of the radius Oz with the positive real axis".

The word “phase” appears 5 times on the Wikipedia page for complex numbers. The word “angle” appears 13 times (searching for “angle” gives 33 results, but 20 of them are for “triangle”). This tells me that when discussing complex numbers, it is much more common to talk about angles than phases.

Similarly, on the Wikipedia page for “Argument (complex analysis)”, the word “phase” appears once and the word “angle” appears 11 times. Notably, the only appearance of “phase” there is a remark that it is sometimes used as a synonym. The entire rest of the article uses “angle”

from swift-numerics.

The word “phase” appears 5 times on the Wikipedia page for complex numbers. The word “angle” appears 13 times

The majority of these are not talking about the argument, though (and when they are, they explicitly say "angle z makes with the real axis" or similar, rather than "angle of z". By contrast, 4/5 uses of "phase" are explicitly talking about "the phase" of a complex value.

Similarly on the Argument page, the one use of phase is "the names magnitude, for the modulus, and phase,[1] for the argument, are sometimes used equivalently," while "angle" is never used as "the angle" of a complex number, but always to describe "the angle made with the real axis":

• the argument of z is the angle between the positive real axis
• the angle φ from the positive real axis to the vector representing z

or an angle as a geometric quantity, separate from any complex value.

I.e. neither of these pages defines or uses "angle" as an alternative for "argument", but both explicitly give that equivalence for "phase".

from swift-numerics.