1
GATE ME 2014 Set 4
MCQ (Single Correct Answer)
+2
-0.6
If $$z$$ is a complex variable, the value of $$\int\limits_5^{3i} {{{dz} \over z}} $$ is
A
$$ - 0.511 - 1.57i$$
B
$$-0.511+1.57i$$
C
$$0.511-1.57i$$
D
$$0.511+1.57i$$
2
GATE ME 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
An analytic function of a complex variable $$z = x + iy$$ is expressed as
$$f\left( z \right) = u\left( {x + y} \right) + iv\left( {x,y} \right),$$ where $$i = \sqrt { - 1} .$$ If $$u(x, y)=$$ $${x^3} - {y^2}$$
then expression for $$v(x,y)$$ in terms of $$x,y$$ and a general constant $$c$$ would be
A
$$xy+c$$
B
$${{{x^2} + {y^2}} \over 2} + c$$
C
$$2xy+c$$
D
$${{{{\left( {x - y} \right)}^2}} \over 2} + c$$
3
GATE ME 2007
MCQ (Single Correct Answer)
+2
-0.6
If $$\phi (x,y)$$ and $$\psi (x,y)$$ are function with continuous 2nd derivatives then $$\phi (x,y)\, + \,i\psi (x,y)$$ can be expressed as an analytic function of x +iy ($$i = \sqrt { - 1} $$) when
A
$${{\partial \phi } \over {\partial x}} = - {{\partial \psi } \over {\partial x}},\,{{\partial \phi } \over {\partial y}} = {{\partial \psi } \over {\partial y}}$$
B
$${{\partial \phi } \over {\partial y}} = - {{\partial \psi } \over {\partial x}},\,{{\partial \phi } \over {\partial x}} = {{\partial \psi } \over {\partial y}}$$
C
$${{{\partial ^2}\phi } \over {\partial {x^2}}} + {{{\partial ^2}\phi } \over {\partial {y^2}}} = {{{\partial ^2}\psi } \over {\partial {x^2}}} + {{{\partial ^2}\psi } \over {\partial {y^2}}} = 1$$
D
$${{\partial \phi } \over {\partial x}} + {{\partial \phi } \over {\partial y}} = {{\partial \psi } \over {\partial x}} + {{\partial \psi } \over {\partial y}} = 0$$
GATE ME Subjects
Turbo Machinery
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12