Complex Variables and Partial Differential Equations (3130005) MCQs

MCQs of Laurent's Series & Residues

Showing 1 to 10 out of 13 Questions
1.

The Laurent series of function fz=1zz-1 for the region z<1 is _____ .

(a)

1-z-z2-......

(b)

1z+1+z+z2-......

(c)

-1z-1-z-z2-......

(d)

none of these

Answer:

Option (c)

2.

The Laurent series of function fz=1zz-1 for the region z-1<1 is _____ .

(a)

1z-1-1+(z-1)-(z-1)2+......

(b)

1z-1+1+(z-1)+(z-1)2+......

(c)

1z-1-1+z-z2+......

(d)

none of these

Answer:

Option (a)

3.

The principal part of Laurent series of fz=ez-1z2 is _____ .

(a)

z

(b)

1z

(c)

1z2

(d)

none of these

Answer:

Option (b)

4.

The laurent series of function zcos1z about z=0 is _____ .

(a)

z+12!1z+14!1z3+16!1z5+......

(b)

z-12!1z+14!1z3-16!1z5+......

(c)

z-121z+141z3-161z5+......

(d)

none of these

Answer:

Option (b)

5.

The residue of fz=e2zz-2 is _____ .

(a)

e

(b)

e2

(c)

e3

(d)

e4

Answer:

Option (d)

6.

The residue of fz=1(z-1)(z-3) for z=1 is _____ .

(a)

-0.5

(b)

0.5

(c)

1

(d)

-1

Answer:

Option (a)

7.

The residue of function fz=ezz3 is _____ .

(a)

-0.5

(b)

0.5

(c)

1

(d)

none of these

Answer:

Option (b)

8.

The residue at z=0 of function fz=z cos1z is _____ .

(a)

0

(b)

1

(c)

-0.5

(d)

0.5

Answer:

Option (c)

9.

The residue at z=0 of function e3z is _____ .

(a)

0

(b)

1

(c)

2

(d)

3

Answer:

Option (d)

10.

What is the value of C:z=1 z4 e3zdz ? Use the laurent's series expansion.

(a)

81πi20

(b)

81πi10

(c)

81πi30

(d)

81πi40

Answer:

Option (a)

Showing 1 to 10 out of 13 Questions