An imaginary operator, also called an i-operator or j-operator, may be understood as follows:
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
|The imaginary operator i rotates the vector OP into OP", and – on a second
application – rotates OP" into OP'