1
GATE ECE 2016 Set 2
Numerical
+2
-0
Consider the complex valued function $$f\left( z \right) = 2{z^3} + b{\left| z \right|^3}$$ where $$z$$ is a complex variable. The value of $$b$$ for which the function $$f(z)$$ is analytic is __________.
2
GATE ECE 2016 Set 1
Numerical
+2
-0
In the following integral, the contour $$C$$ encloses the points $${2\pi j}$$ and $$-{2\pi j}$$. The value of the integral $$- {1 \over {2\pi }}\oint\limits_c {{{\sin z} \over {{{\left( {z - 2\pi j} \right)}^3}}}} dz$$ is ___________.
3
GATE ECE 2015 Set 3
+2
-0.6
If $$C$$ is a circle of radius $$r$$ with centre $${z_0}$$ in the complex $$z$$-plane and if $$'n'$$ is a non-zero integer, then $$\oint\limits_c {{{dz} \over {{{\left( {z - {z_0}} \right)}^{n + 1}}}}}$$ equals
A
$$2\pi nj$$
B
$$0$$
C
$${{nj} \over {2\pi }}$$
D
$$2\pi n$$
4
GATE ECE 2015 Set 2
Numerical
+2
-0
Let $$f\left( z \right) = {{az + b} \over {cz + d}}.$$ If $$f\left( {{z_1}} \right) = f\left( {{z_2}} \right)$$ for all $${z_1} \ne {z_2}.\,\,a = 2,\,\,b = 4$$ and $$C=5,$$ then $$d$$ should be equal to
GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics
EXAM MAP
Joint Entrance Examination