Origin: Latin suffix -ary
Imaginary has 4 different meanings across 2 categories:
(mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1
"The complex solution to the quadratic equation involved an imaginary component."
Imagination; fancy.
"The old tale was nothing more than a collection of imaginary stories told by firelight."
Existing only in the imagination.
"The imaginary friend he played with all afternoon was never real, existing only in his mind."
In plain English: Imaginary means something that exists only in your mind and is not real.
"The child played happily with his imaginary friend all afternoon."
The word imaginary comes from Latin imāginārius, meaning "relating to images" or "fancied." Its specific mathematical sense originated with René Descartes in 1637 when he used it derogatorily to describe non-real roots of polynomials.