phase number ⇒ phase
phase returns the phase of number (the angle part of its polar representation) in radians, in the range
-\pi (exclusive) if minus zero is not supported, or -\pi (inclusive) if minus zero is supported,
to \pi (inclusive). The phase of a positive
real
number is zero; that of a negative
real
number is \pi. The phase of zero is defined to be zero.
If number is a complex float, the result is a float of the same type as the components of number. If number is a float, the result is a float of the same type. If number is a rational or a complex rational, the result is a single float.
The branch cut for phase lies along the negative real axis, continuous with quadrant II. The range consists of that portion of the real axis between -\pi (exclusive) and~\pi (inclusive).
The mathematical definition of phase is as follows:
(phase x) = (atan (imagpart x) (realpart x))
(phase 1) ⇒ 0.0s0
(phase 0) ⇒ 0.0s0
(phase (cis 30)) ⇒ -1.4159266
(phase #c(0 1)) ⇒ 1.5707964
Should signal type-error if its argument is not a number. Might signal arithmetic-error.