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.