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. |
Let z and ω be complex numbers satisfying zz̅+ω\(\overline{\omega}\)=100. If |z|,|ω|∈I, then find the minimum possible value of the expression |z+ω|. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 2. |
Let z and ω be complex numbers such that ω has non-zero imaginary part and z≠1. If the expression (ω-\(\overline{\omega}\)z)/(1-z) is purely real, then find the set of values of z. |
| A. | {z : |z|=1} |
| B. | {z : z=z̅} |
| C. | {z : z≠1} |
| D. | {z : |z|=1, z≠1} |
| Answer» E. | |
| 3. |
Let zz̅=64, and ω\(\overline{\omega}\)=36. Find the maximum possible value of |z+ω|. |
| A. | 8 |
| B. | 10 |
| C. | 12 |
| D. | 14 |
| Answer» E. | |
| 4. |
If z and ω are the complex conjugates of each other, then find the value of (lnz+lnω)/ln|z|. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 5. |
The hyperbola, x2–y2=1 can be represented on the Argand Plane by which of the following equations? |
| A. | z2-z̅2=1 |
| B. | z2+z̅2=1 |
| C. | z2-z̅2=2 |
| D. | z2+z̅2=2 |
| Answer» E. | |
| 6. |
If the complex numbers (x2-3x+2)+i(y2-11y+40) and (x2-6x+8)+i(y2-9x+10) are conjugates of each other, Then what is the value of |x+iy|? |
| A. | 131/2 |
| B. | 191/2 |
| C. | 231/2 |
| D. | 291/2 |
| Answer» E. | |
| 7. |
If a complex number z, with integral real and imaginary parts, satisfies z2+ z̅2=16, then find the value of |z|. |
| A. | 21/2 |
| B. | 4 |
| C. | 81/2 |
| D. | 101/2 |
| Answer» E. | |
| 8. |
Let z=sinx+icos2x and ω=cosx-isin2x. Then for what values of x are z and ω conjugate of each other? |
| A. | x = nπ |
| B. | x = 0 |
| C. | x = (n+1/2)π |
| D. | no value of x |
| Answer» E. | |
| 9. |
For a complex number z, if Re(z) and Im(z) are the roots of x2-7x+12=0 and z+z̅ is one of the roots of x2–10x+16=0, then, find Re(z)-Im(z). |
| A. | 1 |
| B. | -1 |
| C. | 3 |
| D. | -3 |
| Answer» B. -1 | |
| 10. |
Consider the complex number z, for which a line segment A is drawn connecting origin and the point z. Also, consider the line segment B connecting origin and z̅. if z = x+iy, and the smaller angle between A and B is α, then select the incorrect option. |
| A. | α=π/2 if x=y |
| B. | α>π/2 if |y|>|x| |
| C. | α=π/2 if x=-y |
| D. | α=2×Arg(z) |
| Answer» E. | |
| 11. |
What is the area of the rectangle whose vertices are the roots of the equation zz̅3+z̅z3=350, given that Re(z) and Im(z) are integers ? |
| A. | 12 |
| B. | 24 |
| C. | 36 |
| D. | 48 |
| Answer» E. | |
| 12. |
For two complex numbers p and q, if Arg(p)-Arg(q)=π/2 as well as |pq|=1, what is the value of p̅q ? |
| A. | -i |
| B. | -1 |
| C. | i |
| D. | 1 |
| Answer» B. -1 | |
| 13. |
Consider the Argand Plane shown below.If another complex number ω=z̅+4i, then find the area of the triangle having O, z and ω as its vertices. |
| A. | 6 |
| B. | 12 |
| C. | 24 |
| D. | 36 |
| Answer» E. | |
| 14. |
Let two complex numbers z and ω satisfy z > \(\overline{\omega}\). Find the value of the expression zIm(ω)+ωIm(z)+zω, if Re(z) and Re(ω) are the roots of the equation x2–5x+6. |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» E. | |
| 15. |
Consider two complex numbers, x and y satisfying |x|=|y| and Arg(x)+Arg(y)=π. What is x in terms of y? |
| A. | y̅ |
| B. | -y̅ |
| C. | y |
| D. | -y |
| Answer» C. y | |