有關 複數函數 既 geometric transformation

可以用 polar form 的形式做 transformation:
f(z) = -3iz - 3
= 3 [cos (-π/2) i sin (-π/2)] z - 3
Note: cos (-π/2) i sin (-π/2) = -i
如此, transformation 可分為三步:

Rotate clockwisely by π/2 (As a result of multiplication of i)
Enlarge by a scale of 3 (As a result of multiplication of 3)
Shift down by 3 units (As a result of subtracting 3)
以下為一例:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Jun08/Crazycomplex2.jpg


2008-06-26 20:28:49 補充：
Sorry for somr mistake:
Step 3 should be shift to "left" instead of "down".
A corrected diagram will be made ASAP.

2008-06-27 15:53:19 補充：
The corrected pic has been updated. Press F5 to reload. Thanks.

大將軍用的是 standard 方法。
> u+iv = (3y-3)+i(-3x)
> thus u = (3y-3) and v = (-3x)
你去到呢度都岩，用 rectangular coordinate 睇，係 4 steps:
http://www.sendspace.com/file/l2w2pf

2008-06-28 14:36:38 補充：
Regarding your question:
>x = a, y = t gives u=3t-3, v=-3a
>跟住我eliminate唔到個t
t is arbitrary, 任意地變, so no need to eliminate
Image of vertical line { (x,y) | x=a } is { (u,v) | v= -3a }(a horizontal line), see?