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[ 本帖最后由 邵逸夫 于 2-7-2006 09:30 AM 编辑 ]

原帖由 邵逸夫 于 4/6/2006 15:11 发表
find the square root of the following complex number
a) 3 - 4i

謝謝

can u help me
setX consists of 50 data with amean of 7 and a standard deviation of 3
a) calculate totalX and totalXpower of 2
b) a number of data,Y,with a sum of 450, amean of 15 and a sum of squares of 5740 are added to set X. claculate the mean and standard deviation when the two sets of data are combined.
c) 2 is added to each value of data in the combined set. calculate the means and standard deviation of this newest set of data.

can u teach me how to do.. thanks

bomber27

3－4i＝4－4i-1
     ＝4－4i+i²
     ＝i²-4i+4
     ＝（i－2）²

dunwan2tellu

can u help me
setX consists of 50 data with amean of 7 and a standard deviation of 3
a) calculate totalX and totalXpower of 2
b) a number of data,Y,with a sum of 450, amean of 15 and a sum of squares of 5740 are added to set X. claculate the mean and standard deviation when the two sets of data are combined.
c) 2 is added to each value of data in the combined set. calculate the means and standard deviation of this newest set of data.

a) total X =  mean x total frequency = 7 x 50 = 350

Var(X) = E(X^2) - (E(X))^2 <==> 3^2 = E(X^2) - (7^2) --> E(X^2) = 58
==> total X^2 = E(X^2) x total frequency = 58 x 50 = 2900

b) frequency of data Y = 450/15 = 30

原本有 50 个 data ,加上 30 个新的 data 就有 80 个 data .他们的和是

Sum = Sum of X + Sum of Y = 350 + 450 = 800

Mean of new data = Sum / total frequency = 800/80 = 10

X^2 + Y^2 = 2900 + 5740 = 8640

Variance = 8640/80 - 10^2 = 8  ==> s.d = sqrt [8] = 2.828

c)let Z be new data , Z = X + 2  ( X = combine data)

E(Z) = E(X+2) = E(X)+2  = 10 + 2 = 12
Var(Z) = Var(X+2) = Var(X) = 8 ==> s.d = 2.828

dunwan2tellu

原帖由 邵逸夫 于 4-6-2006 03:11 PM 发表
find the square root of the following complex number
a) 3 - 4i

謝謝

你要找

Sqrt [ 3 - 4i ] = ?

但是你可以猜得出答案应该是 a - bi 的 pattern .所以

Let Sqrt [ 3 - 4i] = a - bi ==> 3 - 4i = (a-bi)^2 = (a^2 - b^2) - 2ab i

compare coefficient a^2 - b^2 = 3 ; ab = 2

之后就 solve simultaneous equation . 得到 a = + - 2 ; b = + - 1

所以答案应该是 2 - i 或　-2 + i

** 注意到

sqrt [ x^2] = x   only if x is positive real number .
sqrt [x^2 ] = -x only if x is negative real number .

But sqrt [ x^2 ] = + - x  when x is imaginary number

[ 本帖最后由 dunwan2tellu 于 4-6-2006 07:11 PM 编辑 ]

原帖由 dunwan2tellu 于 4/6/2006 19:04 发表

a) total X =  mean x total frequency = 7 x 50 = 350

Var(X) = E(X^2) - (E(X))^2 <==> 3^2 = E(X^2) - (7^2) --> E(X^2) = 58
==> total X^2 = E(X^2) x total frequency = 58 x 50 = 2900
...

this is how to find out d? u not very understand..... can explain more...

and then the question b) the answer there standard deviation how to find out? can do more detail...

thx...

dunwan2tellu

X 原本有 50 个 data , 平均是 7 。表示这 50 个 data 的和是 50 x 7 = 350

已知 standard deviation = 3 , 所以 variance = 9 . 从 variance 的 formula ,

Var(X) = E(X^2) - ((E(X))^2  

再不然就用 Variance X = (Sum X^2)/ n  -  [(Sum X)/n ]^2

而且 (Sum X)/n = mean = 7 , n = 50

所以 Variance = 9 = (Sum X^2)/50  -  7^2  ==> Sum X^2 = 2900

b) 假设另一个 data 是 set Y .已知 Sum Y = 450 , mean Y = 15 , Sum Y^2 = 5740 .

所以 set Y 共有 450/15 = 30 个 data .

现在新的 data 是 X + Y .(注意到 X 有 50 个 data , Y 有 30 个 data ,X + Y 共有 80 data )

mean X + Y = Sum (X+Y)/n = (Sum X + Sum Y)/ 80 = (350 + 450)/80 = 10

variance (X+Y) = Sum(X^2 + Y^2)/ n - ((Sum(X+Y))/n)^2
               = (2900 + 5740)/80 - 10^2
               = 8

所以 standard deviation (X+Y) = Sqrt [ Variance(X+Y)] = Sqrt[8] = 2.828

ok 吗?

[ 本帖最后由 dunwan2tellu 于 4-6-2006 09:06 PM 编辑 ]

原帖由 dunwan2tellu 于 4/6/2006 21:05 发表
X 原本有 50 个 data , 平均是 7 。表示这 50 个 data 的和是 50 x 7 = 350

已知 standard deviation = 3 , 所以 variance = 9 . 从 variance 的 formula ,

Var(X) = E(X^2) - ((E(X))^2  

再不然就用 V ...

wat is sqrt?

dunwan2tellu

原帖由 ~ciyun~ 于 5-6-2006 12:44 PM 发表

wat is sqrt?

square root / punca kuasa dua / 平方根　

√ 2 = 1.414
√ 36 = 6

[ 本帖最后由 dunwan2tellu 于 5-6-2006 01:16 PM 编辑 ]

原帖由 dunwan2tellu 于 5/6/2006 13:13 发表


square root / punca kuasa dua / 平方根　

√ 2 = 1.414
√ 36 = 6

oh i know la.. thx...... so next time got question don't know do can i ask u?

hamilan911

原帖由 ~ciyun~ 于 5-6-2006 10:34 PM 发表

oh i know la.. thx...... so next time got question don't know do can i ask u?

楼上的，有题目当然很欢迎啊。。。这里讨论的人不多，希望你可以加入。。
不过下次最好用中文发表。。

邵逸夫

原帖由 dunwan2tellu 于 4-6-2006 07:09 PM 发表


你要找

Sqrt  = ?

但是你可以猜得出答案应该是 a - bi 的 pattern .所以

Let Sqrt  = a - bi ==> 3 - 4i = (a-bi)^2 = (a^2 - b^2) - 2ab i

compare coefficient a^2 - b^2 = 3 ; ab = 2

...

謝謝你！！！
我會了

我知道啦！用华语问对吗？没问题！！！！！

pisgon

ln x = e^(-x),x=?

dunwan2tellu

原帖由 pisgon 于 10-6-2006 09:03 PM 发表
ln x = e^(-x),x=?

别开玩笑了。这题没有 elementary solution ,只能用 numerical analysis 的方法来做。i.e Newton Rapson Method .

我用 mathematica 来 check 得到 x = 1.3098 ...

pisgon

原帖由 dunwan2tellu 于 10-6-2006 09:31 PM 发表


别开玩笑了。这题没有 elementary solution ,只能用 numerical analysis 的方法来做。i.e Newton Rapson Method .

我用 mathematica 来 check 得到 x = 1.3098 ...

答案我也知道!

真的没方法做的吗?

dunwan2tellu

原帖由 pisgon 于 11-6-2006 04:06 PM 发表

答案我也知道!

真的没方法做的吗?

类似这样的 equation 都解不到的

sin 2x = x  , e^x = 1/x

这些看起来 non-homogeneous 的 equation ，除了 numerical analysis ,应该没有其他方法。如果有，记得告诉我

pisgon

原帖由 dunwan2tellu 于 11-6-2006 04:17 PM 发表


类似这样的 equation 都解不到的

sin 2x = x  , e^x = 1/x

这些看起来 non-homogeneous 的 equation ，除了 numerical analysis ,应该没有其他方法。如果有，记得告诉我

放心吧!有的时候一定贴上来分享!

开学时去问老师~~

邵逸夫

頂帖子。。。。

dunwan2tellu

原帖由 邵逸夫 于 12-6-2006 03:57 PM 发表
頂帖子。。。。

如果没有问题的话，你一直顶帖子也没有用