MCQOPTIONS
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MCQOPTIONS
This section includes 15 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) ωr-1 if ω is a complex nth root of unity. |
| A. | n(n+1)a/2 |
| B. | ωr-1 if ω is a complex nth root of unity.a) n(n+1)a/2b) nb/(1-n) |
| C. | na/(ω-1) |
| D. | n(n+1)a/(ω-1) |
| Answer» D. n(n+1)a/(ω-1) | |
| 3. |
If ω 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+ω |
| B. | x+ω2 |
| C. | (x+ω)(x+ω2) |
| D. | (x–ω)(x–ω2) |
| 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 ω and ω2 be the non-real cube roots of unity and 1/(a+ω)+1/(b+ω)+1/(c+ω)=2ω2 and 1/(a+ω2)+1/(b+ω2)+1/(c+ω2)=2ω, 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)+|Im(i1/2)|. |
| A. | -1, 1 |
| B. | 0, √2 |
| C. | 0, 1 |
| D. | 1, √2 |
| Answer» C. 0, 1 | |
| 7. |
If α,β,ȣ are the roots of equation x3–3x2+3x+7=0 and ω is cube root of unity, then evaluate (α-1)/(β-1)+(β-1)/(ȣ-1)+(ȣ-1)/(α-1). |
| A. | ω |
| B. | ω2 |
| C. | 3ω |
| D. | 3ω2 |
| Answer» E. | |
| 8. |
Find the value of (1+ω)(1+ω2)(1+ω4)(1+ω8)…to 2n factors. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 9. |
For integral x,y,z, find the range of |x+yω+zω2| 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(3kπ/10)+isin(2kπ/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(3kπ/10)+isin(2kπ/10), then is it true that for each zk, there exists zj satisfying zk× zj=1? |
| A. | True |
| B. | False |
| Answer» B. False | |
| 14. |
In the Argand Plane shown below, a,b,c,d are the 4-th roots of 16. Find the area of the closed Polygon having a,b,c,d as its vertices. |
| A. | 2 sq. units |
| B. | 4 sq. units |
| C. | 8 sq. units |
| D. | 16 sq. units |
| Answer» D. 16 sq. units | |
| 15. |
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 | |