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. |
Let z and be complex numbers satisfying zz + ( overline{ omega} )=100. If |z|,| | I, then find the minimum possible value of the expression |z+ |. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 2. |
Let z and be complex numbers such that has non-zero imaginary part and z 1. If the expression ( - ( overline{ omega} )z)/(1-z) is purely real, then find the set of values of z. |
| A. | {z : |z|=1} |
| B. | {z : z=z } |
| C. | {z : z 1} |
| D. | {z : |z|=1, z 1} |
| Answer» E. | |
| 3. |
Let zz =64, and ( overline{ omega} )=36. Find the maximum possible value of |z+ |. |
| A. | 8 |
| B. | 10 |
| C. | 12 |
| D. | 14 |
| Answer» E. | |
| 4. |
If z and are the complex conjugates of each other, then find the value of (lnz+ln )/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. | z<sup>2</sup>-z <sup>2</sup>=1 |
| B. | z<sup>2</sup>+z <sup>2</sup>=1 |
| C. | z<sup>2</sup>-z <sup>2</sup>=2 |
| D. | z<sup>2</sup>+z <sup>2</sup>=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 &vert;x+iy&vert;? |
| A. | 13<sup>1/2</sup> |
| B. | 19<sup>1/2</sup> |
| C. | 23<sup>1/2</sup> |
| D. | 29<sup>1/2</sup> |
| Answer» E. | |
| 7. |
If a complex number z, with integral real and imaginary parts, satisfies z2+ z 2=16, then find the value of &vert;z&vert;. |
| A. | 2<sup>1/2</sup> |
| B. | 4 |
| C. | 8<sup>1/2</sup> |
| D. | 10<sup>1/2</sup> |
| Answer» E. | |
| 8. |
Let z=sinx+icos2x and =cosx-isin2x. Then for what values of x are z and conjugate of each other? |
| A. | x = n |
| B. | x = 0 |
| C. | x = (n+1/2) |
| 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+z 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 z . if z = x+iy, and the smaller angle between A and B is , then select the incorrect option. |
| A. | = /2 if x=y |
| B. | > /2 if &vert;y&vert;>&vert;x&vert; |
| C. | = /2 if x=-y |
| D. | =2 Arg(z) |
| Answer» E. | |
| 11. |
What is the area of the rectangle whose vertices are the roots of the equation zz 3+z z3=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)= /2 as well as &vert;pq&vert;=1, what is the value of p q ? |
| A. | -i |
| B. | -1 |
| C. | i |
| D. | 1 |
| Answer» B. -1 | |
| 13. |
Let two complex numbers z and satisfy z > ( overline{ omega} ). Find the value of the expression zIm( )+ Im(z)+z , if Re(z) and Re( ) are the roots of the equation x2 5x+6. |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» E. | |
| 14. |
Consider two complex numbers, x and y satisfying &vert;x&vert;=&vert;y&vert; and Arg(x)+Arg(y)= . What is x in terms of y? |
| A. | y |
| B. | -y |
| C. | y |
| D. | -y |
| Answer» C. y | |