28. The locus of the points z such that /z 3/ = 2 is A. x² + y = 4 C. x* + y - 6y + 5 = 0 D. x+ y- 6x + 13 = 0 B. x² + y- - 6x + 5 = 0 ,2 V3 29. In the Argand diagram, the point representing the omnlex numher: -+ i

Advanced Engineering Mathematics
10th Edition
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve Q28, 29, 27 explaining detailly each step

19. The modulus of the complex number
3+i .
IS
2-i
3.
D.
9.
10
A.-
B. V2 C.
|
4
3
V3-i
20. If z =
1+i
,\z*| =
%3D
A. 4/2 B. 8 C. 4 D. V3
3/2
3V2
21. The argument of the complex number
is:
is:
2
TT
A.
4
B.- C. -Tt
D.
4
22. If z = v3 + i, arg z° =
%3D
A.
3
B.- C. T D. 2n
|
6.
2i
23. The argument of
is:
1-V3i
- 5T
5Tt
D.
TT
A.
B.
C.
3
24. Given that |z|= 2 and arg z =
- TC
-, Z
6
c.
3i
1
A.
2 2
B.1 - V3i
D. V3+i
2
2
25. Given that -V2 + v2i = r (cos0 + isin0) the values of r and 0 are:
%3D
3
A. rF v2, 0 = v2i B. 1 -V3i C.
i D. V3 - i
2 2
26. The locus (1oci) of the point representing the complex number z such that Im(z+
1
30 is
(are): A. y = 0, x²+y = 1 B. y =0, x² + y² = 0C. x² +y° = 1 D. y =0
27. The locus of the points z such that arg (z - 2 + 3i) = is
4
A. x-y+ 1= 0 B. x-2 0 C. x- y = 5 = 0 D. y-3 = 0
28. The locus of the points z such that /z 3/ =2 is
A. x² + y = 4
C. x² + y – 6y + 5 = 0 D. x²+ y - 6x + 13 = 0
|
B. x + y - 6x + 5 = 0 .
%3D
29. In the Argand diagram, the point representing the complex number: + i
1
2
(i)
Lies on the circle /Z/ = 1
Lies on the half line arg Z= 60°
(ii)
(ii)
Lies on the straight line /Z/ = /Z - 1/
A. (i), (ii) and (iii) are correct. B. only (i) and (ii) are corrct
C. only (ii) and (iii) are correct
D. only (i) is correct
is
Transcribed Image Text:19. The modulus of the complex number 3+i . IS 2-i 3. D. 9. 10 A.- B. V2 C. | 4 3 V3-i 20. If z = 1+i ,\z*| = %3D A. 4/2 B. 8 C. 4 D. V3 3/2 3V2 21. The argument of the complex number is: is: 2 TT A. 4 B.- C. -Tt D. 4 22. If z = v3 + i, arg z° = %3D A. 3 B.- C. T D. 2n | 6. 2i 23. The argument of is: 1-V3i - 5T 5Tt D. TT A. B. C. 3 24. Given that |z|= 2 and arg z = - TC -, Z 6 c. 3i 1 A. 2 2 B.1 - V3i D. V3+i 2 2 25. Given that -V2 + v2i = r (cos0 + isin0) the values of r and 0 are: %3D 3 A. rF v2, 0 = v2i B. 1 -V3i C. i D. V3 - i 2 2 26. The locus (1oci) of the point representing the complex number z such that Im(z+ 1 30 is (are): A. y = 0, x²+y = 1 B. y =0, x² + y² = 0C. x² +y° = 1 D. y =0 27. The locus of the points z such that arg (z - 2 + 3i) = is 4 A. x-y+ 1= 0 B. x-2 0 C. x- y = 5 = 0 D. y-3 = 0 28. The locus of the points z such that /z 3/ =2 is A. x² + y = 4 C. x² + y – 6y + 5 = 0 D. x²+ y - 6x + 13 = 0 | B. x + y - 6x + 5 = 0 . %3D 29. In the Argand diagram, the point representing the complex number: + i 1 2 (i) Lies on the circle /Z/ = 1 Lies on the half line arg Z= 60° (ii) (ii) Lies on the straight line /Z/ = /Z - 1/ A. (i), (ii) and (iii) are correct. B. only (i) and (ii) are corrct C. only (ii) and (iii) are correct D. only (i) is correct is
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