The contour integral $$\oint\limits_{\text{C}} {{{\text{e}}^{\frac{1}{{\text{z}}}}}{\text{dz}}} $$   with C as the counter-clockwise unit circle in the z-plane is equal to

The contour integral $$\oint\limits_{\text{C}} {{{\text{e}}^{\frac{1}{{\text{z}}}}}{\text{dz}}} $$   with C as the counter-clockwise unit circle in the z-plane is equal to Correct Answer $$2\pi \sqrt { - 1} $$

Bissoy MCQ

Related Questions

The values of the integral $$\frac{1}{{2\pi {\text{j}}}}\oint\limits_{\text{c}} {\frac{{{{\text{e}}^{\text{z}}}}}{{{\text{z}} - 2}}{\text{dz}}} $$    along a closed contour c in anti-clockwise direction for
i. the point z0 = 2 inside the contour c, and
ii. the point z0 = 2 outside the contour c, respectively, are
Using Cauchy's integral theorem, the value of the integral (integration being taken in counterclockwise direction) $$\oint\limits_{\text{c}} {\frac{{{{\text{z}}^3} - 6}}{{3{\text{z}} - {\text{i}}}}{\text{dz}}} $$   is
With respect to the numerical evaluation of the definite integral $${\text{K}} = \int_{\text{a}}^{\text{b}} {{{\text{x}}^2}{\text{dx,}}} $$   where a and b are given, which of the following statements is/are TRUE?
I. The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.
II. The value of K obtained using the Simpson's rule is always equal to the exact value of the definite integral.
A path AB in the form of one quarter of a circle of unit radius is shown in the figure. Integration of (x + y)2 on path AB traversed in a counterclockwise sense is
Calculus mcq question image
If the semi-circular contour D of radius 2 is as shown in the figure, then the value of the integral $$\oint\limits_{\text{D}} {\frac{1}{{\left( {{{\text{s}}^2} - 1} \right)}}{\text{ds}}} $$   is
Complex Variable mcq question image
The value of the contour integral in the complex plane $$\oint {\frac{{{{\text{z}}^3} - 2{\text{z}} + 3}}{{{\text{z}} - 2}}{\text{dz}}} $$    along the contour |z| = 3, taken counter-clockwise is
Steps are given to draw involute of given circle. Arrange the steps f C is the centre of circle and P be the end of the thread (starting point). i. Draw a line PQ, tangent to the circle and equal to the circumference of the circle. ii. Draw the involute through the points P1, P2, P3 ……..etc. iii. Divide PQ and the circle into 12 equal parts. iv. Draw tangents at points 1, 2, 3 etc. and mark on them points P1, P2, P3 etc. such that 1P1 =P1l, 2P2 = P2l, 3P3= P3l etc.
Which two classes use the Shape class correctly?
A. public class Circle implements Shape { private int radius; }B. public abstract class Circle extends Shape { private int radius; }C. public class Circle extends Shape { private int radius; public void draw(); }D. public abstract class Circle implements Shape { private int radius; public void draw(); }E. public class Circle extends Shape { private int radius; public void draw() { /* code here */ } }F. public abstract class Circle implements Shape { private int radius; public void draw() { /* code here */ } }
The value of the integral $$\oint\limits_C {\frac{{{e^z}\sin z}}{{{z^2}}}} dz,$$   where the contour C is the unit circle: |z - 2| = 1, is
Let z be a complex variable. For a counterclockwise integration around a unit circle C, centered at origin.
$$\oint_{\text{c}} {\frac{1}{{5{\text{z}} - 4}}{\text{dz}}} = {\text{A}}\pi {\text{i}}$$     the value of A is