1
GATE EE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Consider the function $$f\left( z \right) = z + {z^ * }$$ where $$z$$ is a complex variable and $${z^ * }$$ denotes its complex conjugate. Which one of the following is TRUE?
A
$$f(z)$$ is both continuous and analytic
B
$$f(z)$$ is continuous but not analytic
C
$$f(z)$$ is not continuous but is analytic
D
$$f(z)$$ is neither continuous nor analytic
2
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Given $$f\left( z \right) = g\left( z \right) + h\left( z \right),$$ where $$f,g,h$$ are complex valued functions of a complex variable $$z.$$ Which ONE of the following statements is TRUE?
A
If $$f(z)$$ is differentiable at $${z_0},$$ then $$g(z)$$ & $$h(z)$$ are also differentiable at $${z_0}.$$
B
If $$g(z)$$ & $$h(z)$$ are differentiable at $${z_0},$$ then $$f(z)$$ is also differentiable at $${z_0}.$$
C
If $$f(z)$$ is continuous at $${z_0},$$ then it is differentiable at $${z_0}.$$
D
If $$f(z)$$ is differentiable at $${z_0},$$ then so are its real and imaginary parts.
3
GATE EE 2014 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Integration of the complex function $$f\left( z \right) = {{{z^2}} \over {{z^2} - 1}},$$ in the counterclockwise direction, around $$\left| {z - 1} \right| = 1,$$ is
A
$$ - \pi i$$
B
$$0$$
C
$$\pi i$$
D
$$2\pi i$$
4
GATE EE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
All the values of the multi valued complex function $${1^i},$$ where $$i = \sqrt { - 1} $$ are
A
purely imaginary
B
real and non negative
C
on the unit circle
D
equal in real and imaginary parts.
GATE EE Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12