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realpart, imagpart

realpart, imagpart Function

Syntax:

realpart number → real

imagpart number → real

Arguments and Values:

number—a number .

real—a real.

Description:

realpart and imagpart return the real and imaginary parts of number respectively. If number is real, then realpart returns number and imagpart returns (* 0 number), which has the effect that the imaginary part of a rational is 0 and that of a float is a floating-point zero of the same format.

Examples:

(realpart #c(23 41)) → 23 
(imagpart #c(23 41.0)) → 41.0 
(realpart #c(23 41.0)) → 23.0 
(imagpart 23.0) → 0.0

Exceptional Situations:

Should signal an error of type type-error if number is not a number .

See Also:

complex

Expanded Reference: realpart, imagpart​

Extracting parts of complex numbers​

realpart and imagpart return the real and imaginary parts of a complex number.

(realpart #c(3 4))
=> 3
(imagpart #c(3 4))
=> 4

(realpart #c(23 41))
=> 23
(imagpart #c(23 41.0))
=> 41.0

Behavior with real numbers​

For a real number, realpart returns the number itself and imagpart returns zero of the same type.

(realpart 5)
=> 5
(imagpart 5)
=> 0

(realpart 3.14)
=> 3.14
(imagpart 3.14)
=> 0.0

(realpart 2/3)
=> 2/3
(imagpart 2/3)
=> 0

Type contagion with float components​

When a complex has a float component, realpart returns a float even if originally specified as an integer.

(realpart #c(23 41.0))
=> 23.0
(imagpart #c(23 41.0))
=> 41.0

Using realpart and imagpart for complex arithmetic​

You can decompose complex numbers for custom operations.

;; Manually compute the magnitude of a complex number
(let ((z #c(3.0 4.0)))
  (sqrt (+ (* (realpart z) (realpart z))
            (* (imagpart z) (imagpart z)))))
=> 5.0

;; Swap real and imaginary parts
(let ((z #c(5 7)))
  (complex (imagpart z) (realpart z)))
=> #C(7 5)

Relationship with complex constructor​

realpart and imagpart are the inverse of complex.

(let ((z #c(10 20)))
  (equal z (complex (realpart z) (imagpart z))))
=> T