Explore topic-wise MCQs in Complex Analysis.

This section includes 13 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.

Find the area of the region common to the sets S1={z C: |z|<4}, S2={z C:Im[(z-1+ 3i)/(1- 3i)]>0} and S3={z C: Re z>0}.

A. 10 /3
B. 20 /3
C. 16 /3
D. 32 /3
Answer» C. 16 /3
Discussion
2.

The area of the region enclosed by the curve zz +a(z +z)+a=0 is 2 . If a2 7a+10=0, find the area of the region enclosed by the curve zz +2a(z +z)+a=0.

A. 4 sq. units
B. 10 sq. units
C. 14 sq. units
D. 22 sq. units
Answer» D. 22 sq. units
Discussion
3.

Describe the region given by |z-i|z||-|z+i|z||=0.

A. real axis
B. imaginary axis
C. circle centered at origin
D. quadrant 2
Answer» B. imaginary axis
Discussion
4.

Find the locus of z/(1-z2), where z lies on the circle of radius 1 centered at origin and z 1.

A. line not passing through origin
B. |z|= 2
C. real axis
D. imaginary axis
Answer» E.
Discussion
5.

Find the area of the region bounded by arg|z| /4 and |z-1|<|z-3|.

A. 1 sq. units
B. 2 sq. units
C. 3 sq. units
D. 4 sq. units
Answer» E.
Discussion
6.

Given a vertex of the square circumscribing the circle |z-1|= 2 as 2+ 3i, which of the following is not a vertex of this square ?

A. (1- 3)+i
B. i 3
C. ( 3+i)-i
D. i 3
Answer» E.
Discussion
7.

Find the area enclosed by the curve formed by iz3+z2 z+i=0.

A. /2
B.
C. 3 /4
D. 2
Answer» C. 3 /4
Discussion
8.

Consider the shape formed by the set of points z= -1/ , where | |=2. Which of the following is incorrect?

A. eccentricity=4/5
B. |z| 3
C. shape is an ellipse
D. major axis is of length=5/2
Answer» E.
Discussion
9.

On the arg and plane, the complex numbers z1, z2, z3, z4 are the vertices of a parallelogram. Evaluate (z4 z1+z2)/z3.

A. 1
B. 2
C. 3
D. 4
Answer» B. 2
Discussion
10.

Find the largest angle of the triangle formed by thevertices z1=8(1-i), z2=8(i-1) andZ3=10+2 7i.

A. n<img alt="Find largest angle of triangle formed by thevertices z1=8(1-i), z2=8(i-1) &amp; Z3=10+2 7i" class="alignnone size-full wp-image-292067" height="202" src="https://www.sanfoundry.com/wp-content/uploads/2020/09/complex-analysis-questions-answers-regions-complex-plane-q4.png" width="207"/>
B. /3 radians
C. 2 /3 radians
D. /2 radians
E. 3 /4 radians
Answer» D. /2 radians
Discussion
11.

Find the area of the region given by 11 &amp;vert;z&amp;vert; 19.

A. 120 sq. units
B. 180 sq. units
C. 240 sq. units
D. 320 sq. units
Answer» D. 320 sq. units
Discussion
12.

The complex number given by [( 3/2)+i/2]5+[( 3/2)-i/2]5 lies, on which of the following regions?

A. imaginary axis
B. real axis
C. first quadrant
D. fourth quadrant
Answer» C. first quadrant
Discussion
13.

What is the shape of the region formed by the set of complex numbers z satisfying &amp;vert;z- &amp;vert; ?

A. circle of radius
B. circle with center
C. disk of radius
D. disk with center
Answer» E.
Discussion