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A point z has been plotted in the complex plane, as shown in figure below.
Complex Variable mcq question image
The plot for point $$\frac{1}{{\text{z}}}$$ is
In the question given below, four sentences are given which may or may not be grammatically correct. From the given options, choose the grammatically correct sentence. A. Literature often portrayed children as one-dimensional, but children are as complex as adults. B. Literature often portrays children as one-dimensional, but children are as complex as adults. C. Literature often portrays children as one-dimensional, but children are so complex as adults. D. Literature often portrays children as one-dimensional, but children are more complex as adults. 
Sentences of a paragraph are given below in jumbled order. Arrange the sentences in the right order to form a meaningful and coherent paragraph. A. This whole process of breakdown of complex components of food into simpler substances is called digestion B. These complex substances cannot be utilized as such.  C. The components of food such as carbohydrates are complex substances. D. So they are broken down into simpler substances.
The below question contains a paragraph of 6 sentences. The first and the sixth sentences are given in the beginning and end and numbered 1 and 6 respectively. The four sentences in the middle are jumbled and labelled P, Q, R and S. Identify the proper order of these four sentences and mark the correct option. 1. In space navigation it is necessary to make complex calculations. P. In addition, it has to enter into the moon's orbit at a precise moment. Q. In other words it has to leave the earth's orbit at a precise moment. R. A rocket has to follow a precise path. S. Computers are able to perform extremely complex calculations. 6. A computer can perform the complex calculations which are necessary to work out the rocket's path precisely.
Contour C in the adjoining figure is described by x2 + y2 = 16. The value $$\oint\limits_{\text{c}} {\frac{{{{\text{z}}^2} + 8}}{{0.5{\text{z}} - 1.5{\text{j}}}}{\text{dz}}} $$    is (Note: $${\text{j}} = \sqrt { - 1} $$ )
Complex Variable mcq question image
The magnitude and phase of the complex Fourier series coefficient ak of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex number, R is the set of purely real numbers, and P is the set of purely imaginary numbers.
Signal Processing mcq question image
Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):
1. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valued.
2. The complex Fourier series coefficients of x(3f) are {3ak} where k is integer valued.
3. The fundamental angular frequency of x(3t) is 6π rad/s.
For the three statements above, which one of the following is correct?
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
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
Let S be the set of points in the complex plane corresponding to the unit circle. (That is, S = {z : |z| = 1}. Consider the function f(z) = zz∗ where z∗ denotes the complex conjugate of z. The f(z) maps S to which one of the following in the complex plane