1
GATE ME 2024
+1
-0.33

Let f(z) be an analytic function, where z = x + iy . If the real part of f(z) is cosh x cos y , and the imaginary part of f(z) is zero for y = 0 , then f(z) is

A

cosh x exp (−iy)

B

cosh z exp z

C

cosh z cos y

D

cosh z

2
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
3
GATE ME 2016 Set 3
+1
-0.3
Solutions of Laplace's equation having continuous second-order partial derivatives are called
A
biharmonic functions
B
harmonic functions
C
conjugate harmonic functions
D
error functions
4
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
$$90$$
GATE ME Subjects
EXAM MAP
Medical
NEET