# Function PHASE

### Syntax

• phase numberphase

### Description

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 `x`) = (atan (imagpart `x`) (realpart `x`))`

### Examples

```
(phase 1)

→
0.0s0

(phase 0)

→
0.0s0

(phase (cis 30))

→
-1.4159266

(phase #c(0 1))

→
1.5707964

```

None.

None.

### Exceptional Situations

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

• {\secref\FloatSubstitutability}

### Notes

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}