如果 f(z) = -3iz -3
咁佢既 geometric transformation 會係點呢？
我咁諗：
if z = x+iy and w=u+iv, then w=-3iz-3 gives
u+iv = (3y-3)+i(-3x)
thus u = (3y-3) and v = (-3x)
to find the image of the line x =a
x = a, y = t gives u=3t-3, v=-3a
跟住我eliminate唔到個t
諗到個頭都大埋…其實我係咪用錯方法？
有關 複數函數 既 geometric transformation
2008-06-26 11:21 pm
回答 (2)
2008-06-27 12:51 am
✔ 最佳答案
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.
參考: My Maths knowledge
2008-06-28 10:36 pm
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?
> 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?
收錄日期: 2021-05-01 09:41:34
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