1
GATE ME 2016 Set 1
+1
-0.3
$$f\left( z \right) = u\left( {x,y} \right) + i\,\,\,\,v\left( {x,y} \right)$$ is an analytic function of complex variable $$z=x+iy$$ , where $$i = \sqrt { - 1}$$ If $$u(x,y)=2xy,$$ then $$v(x,y)$$ may be expressed as
A
$$- {x^2} + {y^2} +$$ constant
B
$${x^2} - {y^2} +$$ constant
C
$${x^2} + {y^2} +$$ constant
D
$$- \left( {{x^2} + {y^2}} \right) +$$ constant
2
GATE ME 2015 Set 1
+1
-0.3
Given two complex numbers $${z_1} = 5 + \left( {5\sqrt 3 } \right)i$$ and $${z_2} = {2 \over {\sqrt 3 }} + 2i,$$ the argument of $${{{z_1}} \over {{z_2}}}$$ in degrees $$i$$
A
$$0$$
B
$$30$$
C
$$60$$
D
$$90$$
3
GATE ME 2014 Set 2
+1
-0.3
An analytic function of a complex variable $$z=x+iy,$$ where $$i = \sqrt { - 1}$$ is expressed as
$$f\left( z \right) = u\left( {x,y} \right) + i\,v\left( {x,y} \right).\,$$ If $$u(x,y)=2xy,$$
then $$v(x,y)$$ must be
A
$${x^2} + {y^2} +$$ constant
B
$${x^2} - {y^2} +$$ constant
C
$$-{x^2} + {y^2} +$$ constant
D
$$-{x^2} - {y^2} +$$ constant
4
GATE ME 2014 Set 1
+1
-0.3
The argument of the complex number $${{1 + i} \over {1 - i}},$$ where $$i = \sqrt { - 1} ,$$ is
A
$$- \pi$$
B
$$- {\pi \over 2}$$
C
$${\pi \over 2}$$
D
$$\pi$$
GATE ME Subjects
Engineering Mechanics
Machine Design
Strength of Materials
Heat Transfer
Production Engineering
Industrial Engineering
Turbo Machinery
Theory of Machines
Engineering Mathematics
Fluid Mechanics
Thermodynamics
General Aptitude
EXAM MAP
Joint Entrance Examination