Explore topic-wise MCQs in Complex Analysis.

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.

In the triangle shown, if the angle corresponding to z3 is said to be π/2, Find a possible value of z3 in terms of z1, z2 and z4.

A. z4+3/5(z2– z1)eiπ/2
B. z4-3/5(z2– z1)eiπ/2
C. z4+3/5(z2– z1)e-iπ/2
D. no such z3 is possible
Answer» E.
Discussion
2.

Find the area of the region common to the sets S1={z∈C: |z|0} and S3={z∈C: Re z>0}.

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

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

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

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
5.

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
6.

Find the area of the region bounded by arg|z|≤π/4 and |z-1|

A. 1 sq. units
B. 2 sq. units
C. 3 sq. units
D. 4 sq. units
Answer» E.
Discussion
7.

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
8.

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

A. π/2
B. π
C. 3π/4
D. 2π
Answer» C. 3π/4
Discussion
9.

Consider the shape formed by the set of points z=ω-1/ω, where |ω|=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
10.

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
11.

Find the equation of the circle passing through the origin and having intercepts a and b on real and imaginary axes, respectively, on the arg and plane.

A. zz̅=a(Im z)–b(Re z)
B. zz̅=a(Im z)+b(Re z)
C. zz̅=a(Re z)–b(Im z)
D. zz̅=a(Re z)+b(Im z)
Answer» E.
Discussion
12.

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

A. π/3 radians
B. 2π/3 radians
C. π/2 radians
D. 3π/4 radians
Answer» D. 3π/4 radians
Discussion
13.

Find the area of the region given by 11≤|z| ≤ 19.

A. 120π sq. units
B. 180π sq. units
C. 240π sq. units
D. 320π sq. units
Answer» D. 320π sq. units
Discussion
14.

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
15.

What is the shape of the region formed by the set of complex numbers z satisfying |z-ω|≤ α?

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