复数练习题加答案.docx

1、复数练习题加答案 复数练习题加答案 例 计算 ?； ?； ? 分析：根据复数加、减法运算法则进行运算。 解：i?6?i. 2?i?7?7i. i?11i. 确定向量所表示的复数 例 如图，平行四边形OABC，顶点O、A、C分别 表示0，3?2i，?2?4i，试求： AO所表示的复数，BC所表示的复数. 对角线CA所表示的复数 对角线OB所表示的复数及OB的长度 分析：要求某个向量对应的复数，只要找出所求的向量的始点和终点。或者用向量的相等直接给出所求的结论 解：AO?OA ?AO所表示的复数为?3?2i ?BC?AO， ?BC所表示的复数为?3?2i CA?OA?OC， ?CA所表示的复数为?

2、5?2i 对角线OB?OA?AB?OA?OC，它所对应的复数为 ?1?6i |OB|?622?37 求正方形的第四个顶点对应的复数 例 复数z1?1?2i，z2?2?i，z3?1?2i，它们在复平面上的对应点是一个正 方形的三个顶点，求这个正方形的第四个顶点对应的复数。 分析1：利用AD?BC或者AB?DC求点D对应的复数。 解法1：设复数z1，z2，z3所对应的点分别为A、B、C，正方形的第四个顶点D对应 的复数为x?yi则 AD?OD?OA? ?i BC?OC?OB1?3i AD?BC， ?i?1?3i. ?x?1?1 ?y?2?3?x?2?y?1 ? 解得? 故点D对应的复数2?i. 分

3、析2：利用正方形的性质，对角钱相等且互相平分，相对顶点连线段的 中点重合，即利用正方形的两条对角线交点是其对称中心求解 解法2：设复数z1，z2，z3所对应的点分别为A、B、C，正方形的第四个顶点D对应 的复数为x?yi 因为点A与点C关于原点对称，所以原点O为正方形的中心 点O也是B与D点的中点，于是由?0 x?2,y?1. 故D对应的复数为2?i. 小结：解题1一定要善于发现问题中可能被利用的条件，寻找最佳的解题方法，解法2利用正方形是如C对称固形，解题思路较巧 根据条件求参数的值 例 已知z1?a2?3?i，z2?a?1?i分别对应向量， OZ1,OZ2，若向量Z2Z1对应的复数为纯虚数

4、，求a的值 分析：Z2Z1对应的复数为纯虚数，利用复数减法先求出Z2Z1对应的复数，再利用复数为纯虚数的条件求解即得 解：设向量Z2Z1对应复数z Z2Z1?OZ1?OZ2 z?z1?z2?a2?3?i?a2?1?i ?i ?i 20?a?a?2?0z 为纯虚数， ? 即?0a?a?6?0 a?1. 求复数的轨迹方程 例 z?r，求2z?3?4i对应的点的轨迹方程 解：?2z?3?4i，则2z3?4i. 又z?r，故有2z?2r. ?2r ?对应点的轨迹是以3?4i为圆心，2r为半径的圆 小结：由减法的几何意义知z?z1表示复平面上两点z，z1间的距离 当z?z1?r，表示复数z对应的点的轨迹

5、是以z1对应的点为圆心，半径为r的圆 当z?z1?z?z2，表示以复数z1，z2的对应点为端点的线段的垂直平分线 求复数的最大值与最小值 例 设复数满足z?4?3i?2?2?z?4?3i，求z的最大值和最小值 分析：仔细地观察、分析等式z?4?3i?2?2?z?4?3i，实质是一实数等式，由其特点，根据实数的性质知若a?a，则a?0，因此已知等式可化为z?4?3i?2?0 解：由已知等式得z?2?0 即z?2?0，它表示的以点P为圆心，半径R?2的圆面 如图可知z?OQ时，z有最大值OP?R?5?2?7；z?OM时z有最小值OP?R?5?2?3 小结：求复数的模的最值常常根据其几何意义，利用图

6、形直观来解 名词的数 一。单向选择题 1. Have you got _? I want to write a letter. A. any paperB. papers C. any papers D. a paper . Have you seen such big _? A. a tomato B. tomato C. tomatoes D. tomatos . They got much _ from those books. A. ideas B. photos C. information D. stories . There are a lot of _ down there b

7、ut hardly any _. A. sheeps, people B. sheep, people C. sheeps, peoples D. sheep, peoples . What can I do for you? - Id like two _. A. bottle of orange B. bottle of orangesC. bottles of orangeD. bottles of oranges . Several _ are talking under the tree. And their _ are swimming in the lake. A. woman,

8、 childrenB. woman, childC. women, children D. women, child . Uncle Wang bought two _ yesterday. A. watchs B. watches C. watch D. watched . Tom has made _ with Jim. A. a friend B. friendsC. friendD. some friends . What can I do for you? Id like two _. A. box of appleB. boxes of applesC. box of apples

9、 D. boxes of apple 10. Let me give you _. A. an adviceB. some advice C. advices D. the advice 11. He has spent a great _ of money on his new house. A. deal B. many C. number D. piece 12. I only realized age when I found I had _. A. much great hair B. a little great hair C. a few grey hairs D. some g

10、rey hair 13. That farmer has many _ on his farm. A. geeesB. goosen C. gooses D. geese 14. When we saw his face, we knew _ was sad. A. some news B. the news C. a newsD. news 15. The dentist didnt tell me how many _ I should pay for pulling out the tooth. A. money B. dollars C. funds D. moneies 16. Be

11、fore we moved in the new house we bought many _. A. furnituresB. furniture C. pieces of furniture D. equipments 17. His friend lost _ nylon stockings yesterday morning. A. two B. a C. a couple of D. a pair of 18. My family raise a lot of _, including two _. A. cattles, cows B. cows, cattle C. cattle

12、, cows D. cow, cattles 19. All the _ are made of _, not plastics. A. glass, glass B. glasses, glass C. glass, glasses D. glasses, glasses 0. A group of _ are eating _ and_ at the foot of the hill. A. sheep, grass, leaves B. sheeps, grasses, leaves C. sheep, grass, leaf D. sheeps, grass, leaf1. About

13、0 _ of the population in our country _ on farms. A. percent, lives B. percents, lives C. percent, liveD. percents, live 2. The number of people invited _ fifty, but a number of them _ absent for different reasons. A. were, was B. was, wasC. was, were D. were, was 3. My fathers _ is grey, but my moth

14、er has a few grey _. A. hair, hairB. hairs, hairs C. hairs, hair D. hair, hairs 4. -How many _ does a cow have? - Four. A. stomaches B. stomachC. stomachs D. stomachies 5. Father went to his doctor for _ about his heart trouble. A. an advice B. advice C. advices D. the advice 6. The _ of buildings a

15、re covered with lots of _. A. roofs, leaves B. rooves, leafs C. roof, leafD. roofs, leafs 7. As is known to us all, _ travels much faster than_. A. lights, sounds B. light, soundC. sound, lightD. sounds, lights 8. -What would you like, sir? - _. A. Two cups of coffees B. Two coffees C. Two cup of co

16、ffeeD. Two cups coffee 9. These _ want to be _ when they grow up. A. girl-students, woman doctorsB. girl-student, woman doctors C. girls-students, women doctors D. girl-students, women doctors 0. What _! Where did you get them? A. a big fish B. big fish C. a piece of fish D. a piece of big fish 1. I

17、 saw _ running about at the foot of the mountain. A. a cattle B. two cattlesC. much cattle D. a head of cattle 2. _! Lets go climbing! A. What a fine weatherB. How fine weatherC. What a fine dayD. How fine day 3. Thanks for giving me _ I wanted. A. the information B. an informationC. the information

18、s D. information 二。填入所给单词的正确形式。 1. I have two . 2. There are many here. 3. I received a lot of Christmas. There are many. Those are enjoying the suise. . A few are drawing on the wall. . . The 10. Yangtze River in one of the longest in China. 三。写出下列单词的复数形式。 match _foot_half _ fish _wish _fox_ piano

19、_ glass_ cattle _ story_ radio_ scarf_ party_ life _photo_ leaf _ boy _ box _ goose_ mouse_ sheep _ shop _ city_ hero _ German_ zoo _ deer _man_ Negro_ baby_ woman_ thief_ tooth_ child_ Chinese_ wife _ policeman_ Japanese_ brush_ tomato_ knife_ factory_ wolf _ monkey_ bamboo _ map _ stomach_ ox_ gir

20、l student _ pencil-box _ man doctor _ woman teacher _ 一、选择题 3i 1复数等于 1i A12iB12iC2iD2i 答案：C 3i42i解析：2i.故选C. 21i 32i32i 2复数 23i23i A0 B C2iD2i 答案：D 32i32i13i13i解析：ii2i. 1323i23i13 z2 3已知z是纯虚数，z等于 1i A2i Bi CiD2i 答案：D 解析：由题意得zai. z22ai， 21i 则a20，a2.有z2i，故选D.若fx3x2x1，则f A2i B0 C2iD答案：B 解析：依题意，fi3i2i1i1

21、i10，选择B. 2i 5复数z在复平面内对应的点位于 1i A第一象限 B第二象限 C第三象限 D第四象限 答案：D 2i13 解析：zi，它对应的点在第四象限，故选D. 1i22 2ib 6表示为abi ia 11 AB CD. 22 答案：A 2ib解析：12i，把它表示为abi的形式，则2，故选A. ia 2 7设i是虚数单位，复数ztan45isin60，则z等于 13i B.3i471D.44答案：B 31 解析：ztan45isin601i，z23i，故选B. 24 83i在复平面内对应的直线的倾斜角为 A. B625 D.6答案：D 35 3i对应的点为，所求直线的斜率为，则倾

22、斜角为，故选D. 36 abi 9设a、b、c、dR，若 cdi Abcad0Bbcad0 Cbcad0Dbcad0 答案：C abiacbdbcadbcad 解析：因为i，所以由题意有0?bcad0. cdicdcdcdcd 1 10已知复数z12i，那么 z55i551255答案：D 525512D.i5B. 1 12i121 i.故选D. z12i1455 解析：由z12i知z12i，于是 z11已知复数z13bi，z212i是实数，则实数b的值为 z2 1 A BC0 D. 6 答案：A z13bii解析：是实数，则实数b的值为6，故选A. z212i512设z是复数，表示满足zn1的

23、最小正整数n，则对虚数单位i， A B CD答案：B 解析：表示in1的最小正整数n，因i4k1，显然n4，即4.故选B. 13 13若z，且4a0x4a1x3a2x2a3xa4，则a2等于 2213 AiB333i 22C633iD333i 答案：B 4r 解析：Tr1Crr，x由4r2得r2， 1322 a2C2i)6i对应的点位于 A第一象限B第二象限 C第三象限D第四象限 答案：B 解析：ABC为锐角三角形， AB90，B90A， cosBsinA，sinBcosA， cosBsinA0，sinBcosA0， z对应的点在第二象限 2bi 15如果复数的实部和虚部互为相反数，那么b等于

24、 12i 22 C D2 33 答案：C 2bi解析： 512i 5522b4b2由b553 13 16设函数fx55x410x310x25x1，则f的值为 22 1331Ai B.i 2222131iD222答案：C 解析：f5 1313 f)5 2222 13 5 221313 i. 2222 17若i是虚数单位，则满足2qpi的实数p，q一共有 A1对 B2对 C3对 D4对 答案：D 22pqq，?p0，?p0，222 解析：由qpi得2pqiqpi，所以?解得?或? ?2pqp.?q0，?q1， ?p2或?1 q?2， ?p2， 或?1 q?2 因此满足条件的实数p，q一共有4对 总

25、结评述：本题主要考查复数的基本运算，解答复数问题的基本策略是将复数问题转化为实数问题来解决，解答中要特 1 别注意不要出现漏解现象，如由2pqp应得到p0或q2 2x20 18已知6的展开式中，不含x的项是，那么正数p的值是 xp27 A1 B C D答案：C 20412 解析：由题意得：C62，求得p3.故选C. p27 总结评述：本题考查二项式定理的展开式，注意搭配展开式中不含x的项，即找常数项 19复数zlgi在复平面内对应的点位于 A第一象限 B第二象限 C第三象限 D第四象限 答案：C 解析：本题考查复数与复平面上的点之间的关系，复数与复平面上的点是一一对应的关系，即zabi，与复平

26、面上的 点Z对应，由zlgi知： alg0，又2x2x122110； 0，即b0.应为第三象限的点，故选C. 20设复数zi在映射f下的象为复数z的共轭复数与i的积，若复数在映射f下的象为12i，则相应的为 AB22i C2i D2i 答案：A 解析：令abi，a，bR，则aii， 映射f下的象为aiiai12i. b11，?b0，?解得?2. ?a2.?a2.? 第卷 二、填空题1已知z是复数，i是虚数单位，若z2i，则z_. 答案：1i 2i 解析：z2i，z1i. 1i22若复数z满足z1i，则其共轭复数z_. 答案：i 1i2解析：zi， 1izi. 23若复数z1429i，z269i，其中i是虚数单位，则复数i的实部为_ 答案：20 解析：ii202i，故i的实部为20. 1ai 24在复平面内，复数对应的点位于虚轴上，则a_