**phase***number*→*phase*

**phase** returns the phase of *number* (the angle part of its polar representation) in radians, in the range `-π`

(exclusive) if minus zero is not supported, or `-π`

(inclusive) if minus zero is supported, to `π`

(inclusive). The phase of a positive *real* number is zero; that of a negative *real* number is `π`

. 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 `-π`

(exclusive) and~`π`

(inclusive).

The mathematical definition of **phase** is as follows:

(phase 1)

→0.0s0

(phase 0)

→0.0s0

(phase (cis 30))

→-1.4159266

(phase #c(0 1))

→1.5707964

None.

None.

Should signal **type-error** if its argument is not a *number*. Might signal **arithmetic-error**.

- {\secref\FloatSubstitutability}

None.

\issue{IEEE-ATAN-BRANCH-CUT:SPLIT} \issue{REAL-NUMBER-TYPE:X3J13-MAR-89} \issue{REAL-NUMBER-TYPE:X3J13-MAR-89} \issue{IEEE-ATAN-BRANCH-CUT:SPLIT}