5條初中數學選擇題，求高手幫助 22分

(1) -1+5i/i+1 + (2i+5)(3i-1)
= -1+5+1+(-6-2i+15i-5)
= 5-6+13i-5
= 6+13i//



(2)I am not sure if the answer is correct or not since I cannot understand the question well in Chinese.

This question is certainly a conditional probability and it should be correct if I didn't get it wrong.

P(Aa | parents can be either AA or Aa)
= P(Aa∩parents can be either AA or Aa)/ P(parents can be either AA or Aa)
= 4/9
1/2(4/9+4/9)*2
= 4/9
1/2(8/9)*2
= 4/9
8/9
= 1/2 (or 0.5)//



(3)Sorry but I just simply cannot understand what (3)(a) to (d) are going on.

圖片參考：http://imgcld.yimg.com/8/n/AD01558457/o/701205300070513873410000.jpg




3)Sorry but what is "極形式" in English???!!!



4) (1+2x+3x^2)(3+2x+x^2)(1+x+x^2)
= (3+2x+x^2+6x+4x^2+2x^3+9x^2+6x^3+3x^4)(1x^2+x+1)
= (3x^4+8x^3+14x^2+8x+3)(x^2+x+1)

In the function, only the quotient of (3x^4)(x) and (8x^3)(x^2) can form x^5.

(3x^4)(x)=3x^5

(8x^3)(x^2)=8x^5

Since 3x^5+8x^5=11x^5, therefore the coefficient of x^5=11//

The answer is (a)11.



5)Again, sorry but what is "極形式" in English???!!!

1. (-1+5i) / (i+1) + (2i+5)(3i-1) = (-1+5i)(i-1) / (i+1)(i-1) + (-6-2i+15i-5)
= (-i+1-5-5i) / (-1-1) + (-11+13i) = (-4-6i) / (-2) -11+13i = 2+3i-11+13i
= -9+16i

2. 父母均擁有顯性基因的特性，即父母的基因可分別是
(a)AA, AA; (b)AA, Aa; (c)Aa, AA; (d)Aa, Aa
如果是情況a，那他們下一代的基因有4個可能性：AA, AA, AA, AA
如果是情況b，那他們下一代的基因也有4個可能性：AA, Aa, AA, Aa
如果是情況c，那他們下一代的基因也有4個可能性：AA, AA, aA, aA
如果是情況d，那他們下一代的基因也有4個可能性：AA, Aa, aA, aa
所以這個體的基因型為Aa的概率=6/(4×4)=6/16=3/8

3-1. 5x^2 -5x -2 / x+1
____________
5x^3 -7x +2
5x^3+5x^2
---------------------
-5x^2 -7x +2
-5x^2 -5x
---------------------
-2x +2
-2x -2
--------------------
4

商式=5x^2-5x-2, 餘式=4

3-2. 很顯然，若複數4+3i的極形式為(r,θ)，r=√(3^2+4^2)=5,
sinθ=3/5, cosθ=4/5, cos(θ+180°)= -cosθ= -4/5
所以答案是d

4. 要在1、2x、3x^2，3、2x、x^2，以及1、x、x^2 裏，
找出能夠乘出x^5的項，
有2x × x^2 × x^2，3x^2 × 2x × x^2和3x^2 × x^2 × x，
它們的和=2x^5+6x^5+3x^5=11x^5，
所以(1+2x+3x^2)(3+2x+x^2)(1+x+x^2)中x^5的系數是11

5. (Z1)^4×(Z2) - 2(Z3) = (√5,25°)^4×(3,120°) - 2(35,-140°)
=[(√5)^4, (25°×4)]×(3,120°) - 2[35, (360°-140°)]
=(25,100°)×(3,120°) - 2(35,220°)
=[(25×3), (100°+120°)] - [(2×35),220]
=(75,220°)-(70,220°)
=[(75-70),220°]
=(5,220°)

2012-06-05 08:06:11 補充：
改正
2.

P(後代有基因型 Aa)
= P(後代有基因型 Aa | 父母都有基因型 AA) × P(父母都有基因型 AA)
+ P(後代有基因型 Aa | 父母有基因型AA 和Aa) × P(父母有基因型AA 和Aa)
+ P(後代有基因型 Aa | 父母都有基因型 Aa) × P(父母都有基因型 Aa)
= 0×(4/9)×(4/9) + 2×(1/2)×(4/9)×(4/9) + (1/2)×(4/9)×(4/9)
= 0 + (16/81) + (8/81)
= 27/81
= 1/3

2012-06-05 08:07:15 補充：
我誤會題意了....