imaginary operator

The imaginary operator i rotates the vector
OP into OP", and – on a second
application – rotates OP" into OP'

Also called an ioperator or joperator.
Consider a vector OP where
O is the origin of a set of Cartesian
coordinates and P is the point (a,
b) – see diagram. Multiplying OP by 1 will
produce a vector OP'; that is, it will rotate OP
through 180° such that OP' = OP.
Now consider a number i (called the imaginary
operator) such that multiplying OP by i produces
OP", a vector perpendicular
to OP. Multiplying OP" by i will
produce OP'. Related entry
• vector analysis
Related category
• COMPLEX
NUMBERS 