首页
外语
计算机
考研
公务员
职业资格
财经
工程
司法
医学
专升本
自考
实用职业技能
登录
外语
If |z| ≤ 1, which of the following statements must be true? Indicate all such statements.
If |z| ≤ 1, which of the following statements must be true? Indicate all such statements.
admin
2017-10-16
43
问题
If |z| ≤ 1, which of the following statements must be true? Indicate all such statements.
选项
A、z
2
≤l
B、z
2
≤z
C、z
3
≤z
答案
A
解析
The condition stated in the question, |z|≤1, includes both positive and negative values of z. For example, both 1/2 and
are possible values of z. Keep this in mind as you evaluate each of the inequalities in the answer choices to see whether the inequality must be true.
Choice A: z
2
≤1. First look at what happens for a positive and a negative value of z for which |z|≤1, say, z =1/2 and z=
. If z = 1/2, then z
2
= 1/4. If z =
, then z
2
=1/4. So in both these cases it is true that z
2
≤1.
Since the inequality z
2
≤1 is true for a positive and a negative value of z, try to prove that it is true for all values of z such that |z|≤1. Recall that if 0≤c≤1, then c
2
≤1. Since 0≤\z\≤1, letting c = \z\ yields \z\
2
≤1. Also, it is always true that \z\
2
= z
2
, and so z
2
≤1.
Choice B: z
2
≤z. As before, look at what happens when z =1/2 and when z=
. If z =1/2, then z
2
=1/4. If z =
, then z
2
=1/4. So when z =1/2, the inequality z
2
≤z is true, and when z =
, the inequality z
2
≤z is false. Therefore you can conclude that if |z|≤1, it is not necessarily true that z
2
≤z.
Choice C: z
3
≤z. As before, look at what happens when z =1/2 and when z =
. If z =1/2, then z
3
=1/8. If z =
, then z
3
=
. So when z =1/2, the inequality z
3
≤z is true, and when z =
, the inequality z
3
≤ z is false. Therefore, you can conclude that if |z|≤1, it is not necessarily true that z
3
≤z.
Thus when \z\≤1, Choice A, z
2
≤1, must be true, but the other two choices are not necessarily true. The correct answer consists of Choice A.
This explanation uses the following strategies.
Strategy 8: Search for a Mathematical Relationship
Strategy 10: Trial and Error
Strategy 13: Determine Whether a Conclusion Follows from the Information Given
转载请注明原文地址:https://kaotiyun.com/show/PgkO777K
本试题收录于:
GRE QUANTITATIVE题库GRE分类
0
GRE QUANTITATIVE
GRE
相关试题推荐
BythetimeIfinishedhighschool,myinterestinanimalshadgrown,andenrolledatauniversitytostudybiology.Ilearneds
WehavequiteabitofinformationaboutancientEgyptianmedicine.Doctors’instructionshavebeenfoundtotellus【56】theydid
WehavequiteabitofinformationaboutancientEgyptianmedicine.Doctors’instructionshavebeenfoundtotellus【56】theydid
WehavequiteabitofinformationaboutancientEgyptianmedicine.Doctors’instructionshavebeenfoundtotellus【56】theydid
Allthefollowingcasesareon-the-jobsmokingexceptthat______.Accordingtothepassage,on-the-jobsmokingaffectsanemplo
ThefactthatAmericanslikeshorteranswerstellsus______.Thepassageindicatesthat______.
Accordingtothepassage,AdamSmithwasthefirstpersonto______.AdamSmithmentionedthenumber4800inorderto______.
I’dappreciate______ifyouwouldliketoteachmehowtousethecomputer.
Thenumberofprimaryschoolsintheruralareas______doublinginthepast50years.
Ifeachsideof△ACDabovehaslength3andifABhaslength1,whatistheareaofregionBCDE?
随机试题
撤销党内职务处分,是指撤销受处分党员由党内选举或者组织任命的党内各种职务。()
在氯碱生产三效四体二段蒸发工序中,一效二次蒸汽送往二效加热室,二效二次蒸汽送往三效加热室,三效二次蒸汽送往四效加热室。()
HaveyoueverwatchedahomeshoppingprogramonTV?Canyoudescribe【C1】______it’sliketoshopathomebytelevision?Haveyo
根据降血糖作用机制,阿卡波糖属于
小儿肺的呼吸功能,下列哪项不正确
下列各项中,会引起应收账款账面价值发生增减变动的有()。
【2015年安徽.判断】教材是教学活动可以利用的唯一资源。()
下列名言与作者的对应关系不正确的一项是()。
Alotofpeoplebelievethattelevisionhasaharmfuleffectonchildren.Afewyearsago,thesamecriticismsweremadeofthe
Politicalinstitutionsdevelopwhenthecomplexityofthesocietyreachesthepointatwhichkinshiporganizationcannolonger
最新回复
(
0
)