已知复数z=bi（b∈R），z-21+i是实数，i是虚数单位．（1）求复数z；（_爱下问搜题

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问题解答题

已知复数z=bi（b∈R），

z-2

1+i

是实数，i是虚数单位．
（1）求复数z；
（2）若复数（m+z）²所表示的点在第一象限，求实数m的取值范围．

答案

（1）∵z=bi（b∈R），∴

z-2

1+i

=

bi-2

1+i

=

(bi-2)(1-i)

(1+i)(1-i)

=

(b-2)+(b+2)i

2

=

b-2

2

+

b+2

2

i．

又∵

z-2

1+i

是实数，∴

b+2

2

=0，

∴b=-2，即z=-2i．

（2）∵z=-2i，m∈R，∴（m+z）²=（m-2i）²=m²-4mi+4i²=（m²-4）-4mi，

又∵复数f（4）所表示的点在第一象限，∴

m2-4＞0

-4m＞0

，…（10分）

解得m＜-2，即m∈（-∞，-2）时，复数f（4）所表示的点在第一象限．

单项选择题

对于动作时间小于0.02s的低压断路器，其瞬动过流脱扣器的整定值应取尖峰电流的（）倍。

A．1.2～1.35

B．1.1～1.35

C．1.5～1.7

D．1.7～2

填空题

Part 2

Questions 9-18

·Read the following passage and answer questions 9-18.
1. When one of your car tires goes flat, there are two things you can do. Groan and change or, if you don’t have a spare, stand helplessly behind the road and hope someone to your rescue. Now comes a third alternative, called Quickwheel. It is designed to get disabled motorists rolling again as quickly as possible.
2. Quickwheel is essentially a tiny trailer — complete with three tough little wheels of it’s own — that support the flat tire and enable the motorist to drive to the service station without losing much time or expending much energy. The product is manufactured in the Netherlands but is owned and marketed by a US company. Quickwheel inc. of Greenwich, Connecticut. According to the firm’s president, Robert Bockweg, the product meets each of the major concerns that consumers associate with flat tires: safety lost time and physical exertion.
3. To use it, motorists simply unfold the product to its fully extended position, set it in front of the disabled tire, drive the car on to the Quickwheel’s ramp and attach a special safety strap over the tire. The tire is then locked, or cradled, in Quickwheel’s metal frame. The device’s three wheels do the rest of work.
4. According to Quckwheel Inc., its product can be driven "four miles" at speeds of up to 45 miles per hour without any noticeable change in the vehicle’s breaking or steer operation. The company also claims that it can be used on just any type of car, jeep, mini-van or trailer.
5. Bockweg says that Quickwheel will be sold in the US, at a price of $150. Distribution agreements now being negotiated should make the product available in Japan, Canada and West Europe in the future.

Questions 9-13

·For questions 9-13, choose the best title for each paragraph from below.
·For each numberedparagraph (1-5), mark one letter (A-G) on the Answer Sheet.
·Do not mark any letter twice.

A. The future marketing of Quickwheel.
B. The advantages of the Quickwheel.
C. How does Quickwheel work
D. The ways of dealing with flat tires.
E. Quickwheel can get disabled motorists rolling again.
F. An introduction of Quickwheel.
G. Why is the Quickwheel invented

Paragraph 5: ______