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#### 12.2.46 complex [Function]

`complex` realpart &optional imagpart ⇒ complex

#### Arguments and Values::

realpart—a real.

imagpart—a real.

complex—a rational or a complex.

#### Description::

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

[Reviewer Note by Barmar: What 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.

#### Examples::

     (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)

#### See Also::

realpart , imagpart

#### Notes::

     #c(a b) ≡ #.(complex a b)