ka'o'ei PA5 experimental cmavo

imaginary i, comma - spherical coordinates: first coordinate gives magnitude (complex modulus/radius) of the number, the second number gives the angle from the positive real axis measured counterclockwise toward the 'positive' imaginary axis (default: in the primary branch/Arg) as measured in some units (which that number should contain; the contextless default will suppose radians); the angle is not normalized.

The number (r, x) = r*e^(i x); this would be denoted by "ry ka'o'ei xy". The angle x is (by default) measured in radians and is not normalized (contains no hidden/inherent multiples of pi); it will canonically be between 0 and tau radians (inclusive on only one side; "tau" here means "tau'u"), but it need not be so restricted; x will almost certainly be real. r is necessarily nonnegative and real. r = 0 implies that (r,x) = 0 (as a complex number - id est: complex zero); r being infinite implies that (r,x) is complex infinity (on the Riemann sphere, for example); in either of these situations, x will default to x = 0 if possible - otherwise, to the least value allowed by its domain which is congruent to 0 modulo tau radians. See also: te'o, ka'o.


In notes:

ka'o
digit/number: imaginary i; square root of -1.