# imaginary operator

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

An imaginary operator, also called an ** i-operator** or

**, is the part of a complex number that defines the magnitude of the part of the complex number at right angles to the real number part. It may be understood as follows: consider a vector**

*j*-operator**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'**.