Complex number arithmetic
(scheme complex) provides the operations specific to complex numbers: constructing them from rectangular or polar form and pulling out their parts.
(import (scheme base) (scheme complex))
(make-rectangular 3 4) ;; => 3+4i
(real-part 3+4i) ;; => 3
(imag-part 3+4i) ;; => 4
(magnitude 3+4i) ;; => 5.0
(angle 0+1i) ;; => 1.5707963267948966 (π/2)make-polar builds a complex number from a magnitude and angle.
6 bindings
Syntax: (angle z) Library: (scheme complex) Description: Returns the angle (argument) of the complex number z in radians. For positive reals, returns 0.0. For negative reals, returns pi. Example: (angle 1.0) => 0.0 (angle -1.0) => 3.141592653589793
Syntax: (imag-part z) Library: (scheme complex) Description: Returns the imaginary part of the complex number z. For real numbers, returns 0 (exact or inexact matching z's exactness). Example: (imag-part 3.0) => 0.0 (imag-part 1+2i) => 2
Syntax: (magnitude z) Library: (scheme complex) Description: Returns the magnitude of the complex number z. For real numbers, equivalent to abs. Example: (magnitude -3.0) => 3.0 (magnitude 3+4i) => 5.0
Syntax: (make-polar r theta) Library: (scheme complex) Description: Returns the complex number r * e^(i*theta). Example: (make-polar 1 0) => 1.0 (make-polar 1 1) => 0.5403023058681398+0.8414709848078965i
Syntax: (make-rectangular x y) Library: (scheme complex) Description: Returns the complex number x + yi. Example: (make-rectangular 1 2) => 1+2i (make-rectangular 3 0) => 3
Syntax: (real-part z) Library: (scheme complex) Description: Returns the real part of the complex number z. For real numbers, returns z unchanged. Example: (real-part 3.0) => 3.0 (real-part 1+2i) => 1