Related Questions

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
The complex function tan h(s) is analytic over a region of the imaginary axis of the complex s-plane if the following is TRUE everywhere in the region for all integers n
As per the RBI Act, 1934, the following functions are described as the functions of a Central Bank:
1. Banking functions
2. Advisory functions
3. Supervisory functions
4. Promotional functions
Identify the correct combination:
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
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
A complex function f(z) = u(x, y) + iv(x, y) and its complex conjugate, f'(z) = u(x, y) - iv(x, y) are both analytic in the entire complex plane, where z = x + iy and $${\text{i}} = \sqrt { - 1} .$$   The function f is then given by
Consider the following assertions.
1. Synthetic apirori judgment is the standard of knowledge.
2. Synthetic a posteriori judgement is the standard of knowledge.
3. Analytic apriori judgement is the standard of knowledge.
4. Analytic a posteriori judgement is the standard of knowledge.
Select the correct answer:
Consider the following assertions
1. Synthetic apriori judgement is the standard of knowledge
2. Synthetic a posteriori judgement is the standard of knowledge.
3. Analytic apriori judgement is the standard of knowledge.
4. Analytic a posteriori judgement is the standard of knowledge
Which one of the following functions is analytic over the entire complex plane?