# VCE Specialist Mathematics/Units 3 and 4: Specialist Mathematics/Complex Numbers

Formal Definition: A complex number is a number comprising a real and imaginary part (${\displaystyle z=x+yi}$), where x and y are real numbers, and i is the standard imaginary unit with the property ${\displaystyle i^{2}=-1,i=\pm {\sqrt {-1}}}$, a property that has led to the discovery of the fundamental theorem of algebra. The complex number field (${\displaystyle \mathbb {R} \in \mathbb {C} }$) is a superset of the real number field.