Complex Transformations

Let a be a complex number.

SCALE(a) If a is imaginary, SCALE(a) is equivalent to
That is, the map zaz
SHIFT(a) Equivalent to SHIFT(RE(a),IM(a))
That is, the map zz+a

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