#### 12.2.49 phase [Function]

`phase` number ⇒ phase

#### Arguments and Values::

number—a number.

phase—a number.

#### Description::

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))`

#### Examples::

     (phase 1) ⇒  0.0s0
     (phase 0) ⇒  0.0s0
     (phase (cis 30)) ⇒  -1.4159266
     (phase #c(0 1)) ⇒  1.5707964

#### Exceptional Situations::

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

#### See Also::

Rule of Float Substitutability