1. (Liaoning College Entrance Examination Volume 20 12) The plural number is equal to (a)

(A) - i(B) + i

(C) 1- i(D) 1+ i

2.(20 13 Quality Inspection of Graduating Class of Senior Middle School in Huangshan City, Anhui Province) If the complex number (aR, I is imaginary unit) is purely imaginary, then the value of real number A is (a).

Article 6, paragraph 2, to article 6, paragraph 3 and article 5, paragraph 4.

3.(20 13 Guangdong senior high school entrance examination) Complex number -i+ equals (a)

(A)2i(B)I(C)0(D)2i

Analysis: -i+ =-i-i=-2i, choose A.

4.(20 13 Guangzhou Senior Three Survey) Given I is an imaginary unit, the point corresponding to the complex number i(2-3i) is located in (a).

(a) the first quadrant (b) the second quadrant

(c) the third quadrant (d) the fourth quadrant

Analysis: i(2-3i)=2i-3i2=3+2i, and its corresponding point is (3,2), which is located in the first quadrant, so A is selected.

5. If i(x+yi)=3+4i, x, yR, then the modulus of the complex number x+yi is (d).

2(B)3(C)4(D)5

Analysis: Method 1∶I(x+yi)= 3+4 I,

-y+xi=3+4i，

x=4，y=-3。

Therefore |x+yi|=|4-3i|=5.

Method 2∶I(x+yi)= 3+4 I,

(-i)i(x+yi)=(-i)(3+4i)=4-3i。

That is, x+yi=4-3i, so |x+yi|=|4-3i|=5. Therefore, D.

6. If (x-i)i=y+2i, x, yR, then the complex number x+yi is equal to (b).

(A)-2+i(B)2+i

1-2i(D) 1+2i

Analysis: ∫(x-I)I = Xi+ 1.

And: (x-i)i=y+2i. From the equation of complex numbers,

So x+yi = 2+i.

So choose B.

7.(20 13 Shandong Volume of College Entrance Examination) Complex number z= (i is an imaginary unit), then |z| is equal to (c).

Article 25 (b) (c) Article 5 (d)

Analysis: z = =-4-3i.

|z|= =5。 So, C.

Second, fill in the blanks

8.(20 13 College Entrance Examination Chongqing Volume) If the complex number z= (i is an imaginary unit), then |z|=.

9.(20 13 college entrance examination Hubei volume) I is the imaginary unit, let the complex number Z 1, and the corresponding points of Z2 on the complex plane are symmetrical about the origin. If z 1=2-3i, then z2=.

Analysis: (2, -3) The symmetry point about the origin is (-2, 3),

z2=-2+3i。

Answer: -2+3i

10.(20 13 Tianjin College Entrance Examination Volume) It is known that A, br and I are imaginary units. If (a+i)( 1+i)=bi, then a+bi=.

Analysis: from (a+I) (1+I) = bi (a-1)+(a+1) I = bi,

Therefore, a- 1 = 0, a+1= b.

The solution is a= 1, b=2,

Therefore, a+bi= 1+2i.

Answer: 1+2i

1 1. If it is defined as = ad-BC (A, b, c and d are complex numbers), then the real part of (I is an imaginary unit) is.

Analysis: From the definition, it can be obtained that =2ii(3-2i)-3i 3i=3+4i, so its real part is 3.

Answer: 3

12. The corresponding point of complex number z= (i is imaginary unit) on the complex plane is located in the fourth quadrant.

Analysis: z = =-I is derived from the meaning of the question, so its * * * yoke complex number =+i, and the corresponding point on the complex plane is located in the first quadrant.

Answer: one

Third, answer questions.

13. It is known that I is an imaginary unit. If the real numbers x and y satisfy (1+i) (x+yi) = (1-i) (2+3i), try to determine the quadrant where the point P(x, y) is located.

Solution: The known equation can be changed to (x-y)+(x+y)i=5+i,

According to the equality of two complex numbers,

X=3，y=-2，

So point p is in the fourth quadrant.