Complex Transformations ☆

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 gºf is F*G.