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Given $${\text{f}}\left( {\text{z}} \right) = \frac{1}{{{\text{z}} + 1}} - \frac{2}{{{\text{z}} + 3}}.$$     If C is a counter clockwise path in the z-plane such that |z + 1| = 1, the value of $$\frac{1}{{2\pi {\text{j}}}}\oint_{\text{C}} {{\text{f}}\left( {\text{z}} \right){\text{dz}}} $$    is

Given $${\text{f}}\left( {\text{z}} \right) = \frac{1}{{{\text{z}} + 1}} - \frac{2}{{{\text{z}} + 3}}.$$     If C is a counter clockwise path in the z-plane such that |z + 1| = 1, the value of $$\frac{1}{{2\pi {\text{j}}}}\oint_{\text{C}} {{\text{f}}\left( {\text{z}} \right){\text{dz}}} $$    is Correct Answer 1

Related Questions

If a + b + c + d = 4, then find the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?
If a + b + c + d = 4, then the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?
Which of the following statements are comes for Network Critical Path? 1. The path of critical activities, which links the start and end events is critical path 2. It is the path of activities having zero float 3. It is the path of events having zero slack 4. The sum of the duration of the critical activities along a critical path gives the duration of the Project
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Two circular dials of exactly the same size are mounted on a wall side by side in such a way that their perimeters touch at one point. Dial 1, which is on the left , spins clockwise around its center , and dial 2 , which is on the right spins counter clockwise around its center . (Assume that there is no friction at the point of contact between the dials.) Each dial is marked on its perimeter at three points that are at equale distances around the points arked ondial 1 are N, O, and P and the points marked on dial 2 are X, Y, and Z. If points O and Z are just meeting at the point of contact between the dials , and if dial 1 spins at the same speed as dial 2, what is the smallest number of revolutions of each dial that will bring O and Z together again?
Consider the line integral $$I = \int_{\text{c}} {\left( {{{\text{x}}^2} + {\text{i}}{{\text{y}}^2}} \right){\text{dz,}}} $$    where z = x + iy. The line c is shown in the figure below
Complex Variable mcq question image
The value of $$I$$ is
The value of the expression $$\frac{{{{\left( {a - b} \right)}^2}}}{{\left( {b - c} \right)\left( {c - a} \right)}} + $$   $$\frac{{{{\left( {b - c} \right)}^2}}}{{\left( {a - b} \right)\left( {c - a} \right)}} + $$    $$\frac{{{{\left( {c - a} \right)}^2}}}{{\left( {a - b} \right)\left( {b - c} \right)}}$$   = ?
Which of the following statements regarding binary counters are correct? (a) Clock inputs of all the flip - flops of a synchronous counter are applied from the same source whereas those in an asynchronous counter are from different sources. (b) The asynchronous counter has ripple effects whereas the synchronous counter does not. (c) Only J-K flip-flops can be used in synchronous counters whereas asynchronous counters can be designed with any kind of flip flops. (d) Latches can be used for designing asynchronous counters. Code :
A 12 MHz clock frequency is applied to a cascaded counter containing a modulus-5 counter, a modulus-8 counter, and a modulus-10 counter. The lowest output frequency possible is ________
The Hamiltonian of a particle is given by $$H = \frac{{{p^2}}}{{2m}} + V\left( {\left| {\overrightarrow {\bf{r}} } \right|} \right) + \phi \left( { + \left| {\overrightarrow {\bf{r}} } \right|} \right)\overrightarrow {\bf{L}} .\overrightarrow {\bf{S}} ,$$        where $$\overrightarrow {\bf{S}} $$ is the spin, $$V\left( {\left| {\overrightarrow {\bf{r}} } \right|} \right)$$  and $$\phi \left( {\left| {\overrightarrow {\bf{r}} } \right|} \right)$$  are potential functions and $$\overrightarrow {\bf{L}} \left( { = \overrightarrow {\bf{r}} \times \overrightarrow {\bf{p}} } \right)$$   is the angular momentum. The Hamiltonian does not commute with