Definition:Complex Number/Wholly Real

Definition
A complex number $z = a + i b$ is wholly real iff $b = 0$.

Also known as
Variants on wholly real are:
 * completely real
 * entirely real

etc.

Some sources gloss over the distinction between a real number and a wholly real complex number and merely refer to a number of the form $z = a + 0 i$ as a real number.