MCQOPTIONS
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MCQOPTIONS
This section includes 14 Mcqs, each offering curated multiple-choice questions to sharpen your Complex Analysis knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Which of the following is not equal to (-1)1/3? |
| A. | -1 |
| B. | (- 3+i)/(2i) |
| C. | ( 3+i)/(2i) |
| D. | ( 3 i)/(2i) |
| Answer» E. | |
| 2. |
Find r=1(ar+b) r-1 if is a complex nth root of unity. |
| A. | n(n+1)a/2 |
| B. | nb/(1-n) |
| C. | na/( -1) |
| D. | n(n+1)a/( -1) |
| Answer» D. n(n+1)a/( -1) | |
| 3. |
If is the complex cube root of unity, then which among the following is a factor of the polynomial x6+ 4x5+3x4+2x3+x+1? |
| A. | x+ |
| B. | x+ <sup>2</sup> |
| C. | (x+ )(x+ <sup>2</sup>) |
| D. | (x )(x <sup>2</sup>) |
| Answer» E. | |
| 4. |
Find the cube root of 8i lying in the first quadrant of the complex plane. |
| A. | i- 3 |
| B. | 2i+ 3 |
| C. | i+2 3 |
| D. | i+ 3 |
| Answer» E. | |
| 5. |
Let and 2 be the non-real cube roots of unity and 1/(a+ )+1/(b+ )+1/(c+ )=2 2 and 1/(a+ 2)+1/(b+ 2)+1/(c+ 2)=2 , then calculate 1/(a+1)+1/(b+1)+1/(c+1). |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 6. |
Find the possible value(s) of Re(i1/2)+&vert;Im(i1/2)&vert;. |
| A. | -1, 1 |
| B. | 0, 2 |
| C. | 0, 1 |
| D. | 1, 2 |
| Answer» C. 0, 1 | |
| 7. |
If , , are the roots of equation x3 3x2+3x+7=0 and is cube root of unity, then evaluate ( -1)/( -1)+( -1)/( -1)+( -1)/( -1). |
| A. | |
| B. | <sup>2</sup> |
| C. | 3 |
| D. | 3 <sup>2</sup> |
| Answer» E. | |
| 8. |
Find the value of (1+ )(1+ 2)(1+ 4)(1+ 8) to 2n factors. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 9. |
For integral x,y,z, find the range of &vert;x+y +z 2&vert; if it is not true that x=y=z. |
| A. | [1, ) |
| B. | [ 3, ) |
| C. | (0, 3) |
| D. | (0, ) |
| Answer» B. [ 3, ) | |
| 10. |
Let a and b be complex cube roots of unity. If x=7a+2b and y=2a+7b, then evaluate xy. |
| A. | 9 |
| B. | 39 |
| C. | 45 |
| D. | 53 |
| Answer» E. | |
| 11. |
Find the value of the expression (-1/2+i 3/2)637+(-1/2-i 3/2)337. |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | i |
| Answer» B. 0 | |
| 12. |
For k=1,2, 9, if we define zk=cos(3k /10)+isin(2k /10), then is it possible that z1 z=zk has no Solution z? |
| A. | True |
| B. | False |
| Answer» C. | |
| 13. |
For k=1,2, 9, if we define zk=cos(3k /10)+isin(2k /10), then is it true that for each zk, there exists zj satisfying zk zj=1? |
| A. | True |
| B. | False |
| Answer» B. False | |
| 14. |
The nth roots of any number are in ____________ |
| A. | arithmetic progression |
| B. | geometric progression |
| C. | harmonic progression |
| D. | no specific pattern |
| Answer» C. harmonic progression | |