Let *a* be a complex number.

SCALE(a) | If a is imaginary, SCALE(a) is equivalent to SCALE(ABS( a), ABS(a))*ROTATE(ARG(a))That is, the map z → az |

SHIFT(a) | Equivalent to SHIFT(RE(a),IM(a))That is, the map z → z+a |

<Note>

The map *z* → *a z *+ *b* is SCALE(*a*)*SHIFT(*b*).

The map *z* → *a*( *z* - *b*) *+ c* is SHIFT(-*b*)*SCALE(*a*)*SHIFT(*c*).

The map *z* → CONJ(*z*) is SCALE(1,-1).

If the transformations that corresponds to the maps *f* and *g* are F and G, respectively,
the transformation corresponding to the composite map *g*º*f* is F*G.