问题 解答题

设复数z=lg(m2-2m-2)+(m2+3m+2)i,试求实数m的取值范围,使得:

(1)z是纯虚数;

(2)z是实数;

(3)z对应的点位于复平面的第二象限.

答案

(1)若z=lg(m2-2m-2)+(m2+3m+2)i是纯虚数,则可得

lg(m2-2m-2)=0
m2+3m+2≠0
,即
m2-2m-2=1
m2+3m+2≠0
,解之得m=3(舍去-1);…(3分)

(2)若z=lg(m2-2m-2)+(m2+3m+2)i是实数,则可得

m2+3m+2=0,解之得m=-1或m=-2…(6分)

(3)∵z=lg(m2-2m-2)+(m2+3m+2)i对应的点坐标为(lg(m2-2m-2),m2+3m+2)

∴若该对应点位于复平面的第二象限,则可得

lg(m2-2m-2)<0
m2+3m+2>0
,即
0<m2-2m-2<1
m2+3m+2>0

解之得-1<m<1-

3
或1+
3
<m<3.…(10分)

完形填空

The Quiet Hero 沉默的英雄
It was Mother’s Day, the day we celebrate everything mothers are and everything we do. But I’ll   1   that Sunday in 2000 was bittersweet for me. As a single mother I   2   to think of my shortcomings — how many evenings I couldn’t spend with my children, and how many things I couldn’t   3   my waitress’ salary to buy.
But what   4   kids I had! My daughter Maria was a senior in college, and Denny was home visiting from his freshman year at Harvard University. They were   5   impolite enough to complain, but there was so much more I   6   I had done for them. I just hoped they   ___7 .
As I walked into the   8   quietly to start breakfast, I was greeted by a vase   9   a dozen red roses! When had Denny possibly slipped down to leave them? But even their delicate beauty was overshadowed by the note sitting beside them, in the quick, manly   10   of an eighteen-year-old. It was about a story that happened between Denny and me long ago. It   11  :
She took a day off from her busy   12   to take the boy to see his hero in the flesh at the stadium. It took 3.5 hours just to get there, and they had to be there early   13   he could see his hero take batting practice.   14   their arrival, she took her hard-earned money to buy an overpriced T-shirt on which was   15   his hero making a diving catch. After the game, of course he had to   16   his hero’s signature, so she stayed with the little boy   17   one in the morning…
It took me long enough to   18   it, but I finally know who the   19   hero is. Mom, I love you!
And suddenly, it was a   20   Mother’s Day, after all.
小题1:
A.admitB.adoptC.deny D.refuse
小题2:
A.intendedB.likedC.tended D.hesitated
小题3:
A.stressB.spareC.strengthen D.spend
小题4:
A.poorB.greatC.faithless D.pretty
小题5:
A.merelyB.usuallyC.neverD.often
小题6:
A.wishedB.hopedC.expected D.desired
小题7:
A.supportedB.understoodC.approved D.disgusted
小题8:
A.1iving-room B.kitchenC.bed loom D.study
小题9:
A.includingB.containingC.possessing D.pinning
小题10:
A.handwritingB.descriptionC.tone D.scratch
小题11:
A.wroteB.recordedC.memorized D.read
小题12:
A.eventB.contentC.schedule D.circumstance
小题13:
A.orB.forC.but D.so
小题14:
A.AtB.InC.On D.By
小题15:
A.impressedB.printedC.presented D.pressed
小题16:
A.buyB.abandonC.get D.swap
小题17:
A.beforeB.untilC.after D.when
小题18:
A.seeB.hearC.realize D.tell
小题19:
A.actualB.trueC.imaginary D.visual
小题20:
A.sadB.bitterC.happy D.exciting
单项选择题