Engineering Mathematics
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Q. Consider the line integral I=∫c(x2+iy2)dz, where z=x+iy. The line c is shown in the figure below

The value of I is

The value of I is
- 12i
- 23i
- 34i
- 45i
Q. Let z=x+iy be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
- The residue of zz2−1 at z=1 is 1/2
- ∮Cz2dz=0
- 12πi∮C1zdz=1
- ¯¯¯z (complex conjugate of z) is an analytical function
Q. The value of the integral ∮Cz+1z2−4dz in counter clockwise direction around a circle C of radius 1 with center at the point z=−2
- πi2
- 2πi
- −πi2
- −2πi
Q. If z is a complex variable, the value of ∫3i5dzz is
- −0.511−1.57i
- −0.511+1.57i
- 0.511−1.57i
- 0.511+1.57i
Q. C is a closed path in the z−plane given by |z|=3. The value of the integral ∮C(z2−z+4jz+2j)dz is
- −4π(1+j2)
- 4π(3+j2)
- −4π(3+j2)
- 4π(1−j2)
Q. An integra I over a counterclockwise circle C is given by I=∮Cz2−1z2+1ezdz
If C is defined as |z|=3, then the value of I is
If C is defined as |z|=3, then the value of I is
- −πisin(1)
- −2πisin(1)
- −3πisin(1)
- −4πisin(1)
Q. Evaluate ∫c1(z−1)3.(z−3)dz
where c is the rectangular region defined by z=0, x=4, y=−1 and y=1
where c is the rectangular region defined by z=0, x=4, y=−1 and y=1
- 1
- 0
- π2i
- π(3+2i)
Q.
In the following integral, th contour C encloses the points 2πj and −2πj.
−12π∮Csinz(z−2πj)3dz
The value of the integral is
- 133.87
Q.
If C denotes the counterclockwise unit circle, the value of the contour integral 12πj∮CRezdz is
- 0.5
Q. The countour C in the adjoining figure is described by x2+y2=16. Then the value of ∫cz2+8(0.5)z−(1.5)jdz


- −2πj
- −2πj
- 4πj
- −4πj