magnitude, angle - magnitude and angle of complex numbers

(import (rnrs))                     ;R6RS
(import (rnrs base))                ;R6RS
(import (scheme r5rs))              ;R7RS
(import (scheme complex))           ;R7RS

(magnitude z)
(angle z)

Return the magnitude and angle of z, respectively.

Most implementations of complex numbers do not store them in polar form but instead use rectangular form. The magnitude can be found using the equation for Euclidean distance: (sqrt (+ (expt (real-part z) 2) (expt (imag-part z) 2))). The angle can be found using atan: (atan (imag-part z) (real-part z)).

These procedures return a single value; a real number.

(angle -1)       =>  3.141592653589793   ; approximately
(magnitude 1+i)  =>  1.4142135623730951  ; approximately
(angle -1.0+0.0i)
        =>  3.141592653589793   ; approximately
(angle -1.0-0.0i)
        =>  -3.141592653589793  ; approximately
        ; if -0.0 is distinguished
(angle +inf.0)  =>  0.0
(angle -inf.0)  =>  3.141592653589793  ; approximately
(angle 0)        =>  &assertion raised
(magnitude 0)    =>  0

These procedures work the same everywhere that they are supported. R7RS implementations may not have support for complex numbers.

This procedure can raise exceptions with the following condition types:

&assertion (R6RS)

The wrong number of arguments was passed or an argument was outside its domain.

R7RS

The assertions described above are errors. Implementations may signal an error, extend the procedure's domain of definition to include such arguments, or fail catastrophically.

abs(3scm), make-rectangular(3scm)

R4RS, IEEE Scheme, R5RS, R6RS, R7RS

These procedures first appeared in R2RS, which used Common Lisp as inspiration for its number system. In Common Lisp these procedures are called abs and phase.

This page is part of the scheme-manpages project. It includes materials from the RnRS documents. More information can be found at https://weinholt.se/scheme/manpages/.