MCQOPTIONS
Saved Bookmarks
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 f(z)=z4+a1z3+a2z2+a3z+a4=0; a1, a2, a3, a4 being real and non-zero. If f has a purely imaginary root, then what is the value of the expression a3/(a1a2)+ a1a4/(a2a3) ? |
| A. | 0 |
| B. | 1 |
| C. | -2 |
| D. | 2 |
| Answer» C. -2 | |
| 2. |
For a R, let f(z)=z5-5z+a. Select the correct statement for satisfying f( )=0. |
| A. | has exactly three possible real values for a>4 |
| B. | has exactly one possible real value for a>4 |
| C. | has exactly three possible real values for a<-4 |
| D. | has exactly one possible real value for -4<a<4 |
| Answer» C. has exactly three possible real values for a<-4 | |
| 3. |
Let f(z)=&vert;1 z&vert;, if zk=cos(2k /10)+isin(2k /10), then find the value of f(z1) f(z2) f(z9). |
| A. | 10 |
| B. | 15 |
| C. | 20 |
| D. | 30 |
| Answer» B. 15 | |
| 4. |
Consider a function f(z) of degree two, having real coefficients. If z1 and z2 satisfying f(z1)=f(z2)=0 are such that Re z1=Re z2=0 and if z3 satisfies f(f(z3))=0, then select the correct statement. |
| A. | Re z<sub>3</sub>=0 |
| B. | Im z<sub>3</sub>=0 |
| C. | Re z<sub>3</sub> Imz<sub>3</sub> 0 |
| D. | Re z<sub>3</sub>=0 and Im z<sub>3</sub>=0 |
| Answer» D. Re z<sub>3</sub>=0 and Im z<sub>3</sub>=0 | |
| 5. |
Let f(z)=&vert;z&vert;2+Re z(2(z+z )+3(z-z )/2i, the find the maximum value of &vert;z&vert;2/f(z). |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 6. |
Find the range of the function defined by f(z)=Re[2iz/(1-z2)]. |
| A. | ( , 0) &Union; (0, ) |
| B. | [2, ) |
| C. | ( , 1] &Union; [1, ) |
| D. | ( , 0] &Union; [2, ) |
| Answer» D. ( , 0] &Union; [2, ) | |
| 7. |
Define f(z)=z2+bz 1=0 and g(z)=z2+z+b=0. If there exists satisfying f( )=g( )=0, which of the following cannot be a value of b? |
| A. | 3i |
| B. | - 3i |
| C. | 0 |
| D. | 3i/2 |
| Answer» E. | |
| 8. |
Let f(z)=arg 1/(1 z), then find the range of f(z) for &vert;z&vert;=1, z 1. |
| A. | (- , /2) |
| B. | (- /2, /2) |
| C. | (- , ) |
| D. | [0, /2) |
| Answer» C. (- , ) | |
| 9. |
Let x, y, z be integers, not all simultaneously equal. If is a cube root of unity with Im( ) 1, and if f(z)=az2+bz+c, then find the range of &vert;f( )&vert;. |
| A. | (0, ) |
| B. | [1, ) |
| C. | ( 3/2, ) |
| D. | [1/2, ) |
| Answer» C. ( 3/2, ) | |
| 10. |
For all complex numbers z satisfying Im(z) 0, if f(z)=z2+z+1 is a real valued function, then find its range. |
| A. | (- , -1] |
| B. | (- , 1/3) |
| C. | (- , 1/2] |
| D. | (- , 3/4) |
| Answer» E. | |
| 11. |
Let f(z)=(z2 z 1)7. If 2+ +1=0 and Im( )>0, then find f( ). |
| A. | 128 |
| B. | -128 |
| C. | 128 <sup>2</sup> |
| D. | -128 <sup>2</sup> |
| Answer» D. -128 <sup>2</sup> | |
| 12. |
For the function f(z)=zi, what is the value of &vert;f( )&vert;+Arg f( ), being the cube root of unity with Im( )>0? |
| A. | e<sup>-2 /3</sup> |
| B. | e<sup>2 /3</sup> |
| C. | e<sup>-2 /3</sup>+2 /3 |
| D. | e<sup>-2 /3</sup>-2 /3 |
| Answer» B. e<sup>2 /3</sup> | |
| 13. |
Let f(z)=z+1/z. What will be the definition of this function in polar form? |
| A. | (r+1/r)cos +i(r-1/r)sin |
| B. | (r-1/r)cos +i(r+1/r)sin |
| C. | (r+1/r)sin +i(r-1/r)cos |
| D. | (r+1/r)sin +i(r-1/r)cos |
| Answer» B. (r-1/r)cos +i(r+1/r)sin | |
| 14. |
Find the domain of the function defined by f(z)=z/(z+z ). |
| A. | Im(z) 0 |
| B. | Re(z) 0 |
| C. | Im(z)=0 |
| D. | Re(z)=0 |
| Answer» C. Im(z)=0 | |