A unit is an element in a ring that has a multiplicative inverse. If is an algebraic
integer which divides every algebraic integer
in the field, is called a unit in that field.
A given field may contain an infinity of units.

The numbers of units in the imaginary quadratic field for , 2, ... are 4, 2, 6, 4, 2, 2, 2, 2, 4, 2, 2, 6, 2, ... (OEIS
A092205). There are four units for , 4, 9, 16, ... (OEIS A000290;
the square numbers), six units for , 12, 27, 48, ... (OEIS A033428;
three times the square numbers), and two units for all other imaginary quadratic
fields, i.e., ,
5, 6, 7, 8, 10, 11, ... (OEIS A092206). The
following table gives the units for small . In this table, is a cube root of unity.