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10. Given that z1 = 1-i and z, = 2 +i, z;- Z2 A. B c- D 4 4 C.- 8 i 5 11. Given that z and Z are coniuoate compleY numb

10. Given that z1 = 1-i and z, = 2 +i, z;- Z2 A. B c- D 4 4 C.- 8 i 5 11. Given that z and Z are coniuoate compleY numb

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve Q10, 11, 12 explaining detailly each step

COMPLEX NUMBERS a) MCQS: 1. (2+3i)(1 – i) = 2. i = A. 2 – 2i B. 2+ 4i C. 5 + i D. – 1+ i %3D A. -1 B. -i С. 1 D. i 3. The imaginary part of i"(2 + V3i) – i(1 – 2i) is: A. V3 –1 B. 0 C. - V3 -1 D. - 4 4. The complex conjugate of (1- i) + (2i - 3)i is: A. -2 -i B. 3 + 2i 5. (V3 + i) + (1 – V3i) = C. 3 – 2i D. -1-2i А. 1 B. -i C. i D. -1 D. + 2 1. A. - -- L 5 2. 1 i C. .=+ 3 3 1 6. 2+i 2 B. - 3 3 5 5 7. If (3 – 2i)z - (7 + 4i) = 0, then z = A. + 13 26 29 B.+ 2i 29 2 C. 1+ 2i D. - -_re 13 13 -1+iv3 8. -1-iv3 A. -1- iv3 B. -(2 + iv/3) C. - (1+ iv3) D. –(1+ iv3) | - 2 2 9. Given that z 2 --1+3i, z+ A. -- B- C-- D-+ 12 4 В. 18 4 C.- 12 7 11 5 5 3 10. Given that Z1 = 1 -i and z = 2 + i, z;-= Z.2 4 A. 5 2 4. B. 5 2 3. C. 5 2 i 5 8. + - i D. 5 5 11. Given that z and Z are conjugate complex numbers, which cne of the following is not always true? A. Re (z) = Re(2) B. Im (z) + Im(2) = 0 C. Re(2) = Im(z) D. (z) 12. The roots cf the equation: z- 6z+ 34 = 0 are A. -2, 8 B. 6- 10i, 6 + 10i C. -4, 16 D. 3 - 5i, 3 + 5i 13. The quadratic equation with 2 -i as one of its roots is: A. x+ 5x – 4 0 B. x- 5x + 4= 0 C. x - 4x + 4 = 0 14. p+ 2 is a root of x-x+ 0. The values of p and q are: (z) D. x² - 4x – 5 = (0 %3D 17 A. p= B. p = 1, q = 5 4. 1 17 C. p 15. Given that 5(a + ib) +3 - 2i = 6i, the values of a and b are: D. p =, G = " 17 2 A. a = -3, b -8 B. a = 8. 5' 3 C. a =, b = = 3 С.а a =, b = 8. 5 1 2 1 16. If (x + iy), the values of x and y are: | 3-i 1+2i 10 7. A. x = B. x = 7, y= 7 C. x 7, y = -7 D. x = -7, y = 7 10 10 17. The complex number -2 + 2i can also be expressed as A. 2 [cos (-) + i sin (-ĐI A. 2 cos (-)+ i sin B. 2 cos () + i sin + i sin () D. 2V2 cos (-) + i sin (-| TT OS C. 2v2 fcos () + i sin ( D.2V2 (cos (-) + isin(-) 3T 4 4 4 18. Find the modulus sroument form of the complex number: z = -V3 - i A. A. 2 [cos +i sm B. z [cos-1sinc 2 cost -i sin TT [ca: COS COS + i sinD. 2 cos- i sin 5TT 74 IN
Transcribed Image Text:COMPLEX NUMBERS a) MCQS: 1. (2+3i)(1 – i) = 2. i = A. 2 – 2i B. 2+ 4i C. 5 + i D. – 1+ i %3D A. -1 B. -i С. 1 D. i 3. The imaginary part of i"(2 + V3i) – i(1 – 2i) is: A. V3 –1 B. 0 C. - V3 -1 D. - 4 4. The complex conjugate of (1- i) + (2i - 3)i is: A. -2 -i B. 3 + 2i 5. (V3 + i) + (1 – V3i) = C. 3 – 2i D. -1-2i А. 1 B. -i C. i D. -1 D. + 2 1. A. - -- L 5 2. 1 i C. .=+ 3 3 1 6. 2+i 2 B. - 3 3 5 5 7. If (3 – 2i)z - (7 + 4i) = 0, then z = A. + 13 26 29 B.+ 2i 29 2 C. 1+ 2i D. - -_re 13 13 -1+iv3 8. -1-iv3 A. -1- iv3 B. -(2 + iv/3) C. - (1+ iv3) D. –(1+ iv3) | - 2 2 9. Given that z 2 --1+3i, z+ A. -- B- C-- D-+ 12 4 В. 18 4 C.- 12 7 11 5 5 3 10. Given that Z1 = 1 -i and z = 2 + i, z;-= Z.2 4 A. 5 2 4. B. 5 2 3. C. 5 2 i 5 8. + - i D. 5 5 11. Given that z and Z are conjugate complex numbers, which cne of the following is not always true? A. Re (z) = Re(2) B. Im (z) + Im(2) = 0 C. Re(2) = Im(z) D. (z) 12. The roots cf the equation: z- 6z+ 34 = 0 are A. -2, 8 B. 6- 10i, 6 + 10i C. -4, 16 D. 3 - 5i, 3 + 5i 13. The quadratic equation with 2 -i as one of its roots is: A. x+ 5x – 4 0 B. x- 5x + 4= 0 C. x - 4x + 4 = 0 14. p+ 2 is a root of x-x+ 0. The values of p and q are: (z) D. x² - 4x – 5 = (0 %3D 17 A. p= B. p = 1, q = 5 4. 1 17 C. p 15. Given that 5(a + ib) +3 - 2i = 6i, the values of a and b are: D. p =, G = " 17 2 A. a = -3, b -8 B. a = 8. 5' 3 C. a =, b = = 3 С.а a =, b = 8. 5 1 2 1 16. If (x + iy), the values of x and y are: | 3-i 1+2i 10 7. A. x = B. x = 7, y= 7 C. x 7, y = -7 D. x = -7, y = 7 10 10 17. The complex number -2 + 2i can also be expressed as A. 2 [cos (-) + i sin (-ĐI A. 2 cos (-)+ i sin B. 2 cos () + i sin + i sin () D. 2V2 cos (-) + i sin (-| TT OS C. 2v2 fcos () + i sin ( D.2V2 (cos (-) + isin(-) 3T 4 4 4 18. Find the modulus sroument form of the complex number: z = -V3 - i A. A. 2 [cos +i sm B. z [cos-1sinc 2 cost -i sin TT [ca: COS COS + i sinD. 2 cos- i sin 5TT 74 IN
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