complex realpart &optional imagpart → complex

realpart — a real.

imagpart — a real.

complex — a rational or a complex.

complex returns a number whose real part is realpart and whose imaginary part is imagpart.

If realpart is a rational and imagpart is the rational number zero, the result of complex is realpart, a rational. Otherwise, the result is a complex.

If either realpart or imagpart is a float, the non-float is converted to a float before the complex is created. If imagpart is not supplied, the imaginary part is a zero of the same type as realpart; i.e., (coerce 0 (type-of realpart)) is effectively used.

Type upgrading implies a movement upwards in the type hierarchy lattice. In the case of complexes, the type-specifier must be a subtype of (upgraded-complex-part-type type-specifier). If type-specifier1 is a subtype of type-specifier2, then (upgraded-complex-element-type 'type-specifier1) must also be a subtype of (upgraded-complex-element-type 'type-specifier2). Two disjoint types can be upgraded into the same thing.

(complex 0) → 0 
(complex 0.0) → #C(0.0 0.0) 
(complex 1 1/2) → #C(1 1/2) 
(complex 1 .99) → #C(1.0 0.99) 
(complex 3/2 0.0) → #C(1.5 0.0)

realpart, imagpart, Section 2.4.8.11 (Sharpsign C)