Complex numbers are the set of numbers that describe all possible points in a two-dimensional space. The two coordinates of a particular point in this space are known as the real and imaginary parts of the complex number that describes that point.

In Guile, complex numbers are written in rectangular form as the sum of
their real and imaginary parts, using the symbol `i`

to indicate
the imaginary part.

3+4i ⇒ 3.0+4.0i (* 3-8i 2.3+0.3i) ⇒ 9.3-17.5i

Polar form can also be used, with an ‘`@`’ between magnitude and
angle,

1@3.141592 ⇒ -1.0 (approx) -1@1.57079 ⇒ 0.0-1.0i (approx)

Guile represents a complex number with a non-zero imaginary part as a pair of inexact rationals, so the real and imaginary parts of a complex number have the same properties of inexactness and limited precision as single inexact rational numbers. Guile can not represent exact complex numbers with non-zero imaginary parts.