1
GATE EE 2012
MCQ (Single Correct Answer)
+2
-0.6
If $$x = \sqrt { - 1} ,\,\,$$ then the value of $${X^x}$$ is
A
$${e^{ - \pi /2}}$$
B
$${e^{ \pi /2}}$$
C
$$x$$
D
$$1$$
2
GATE EE 2012
MCQ (Single Correct Answer)
+2
-0.6
Given $$f\left( z \right) = {1 \over {z + 1}} - {2 \over {z + 3}}.$$ If $$C$$ is a counterclockwise path in the $$z$$-plane such that
$$\left| {z + 1} \right| = 1,$$ the value of $${1 \over {2\,\pi \,j}}\oint\limits_c {f\left( z \right)dz} $$ is
A
$$-2$$
B
$$-1$$
C
$$1$$
D
$$2$$
3
GATE EE 2011
MCQ (Single Correct Answer)
+2
-0.6
A point $$z$$ has been plotted in the complex plane as shown in the figure below GATE EE 2011 Engineering Mathematics - Complex Variable Question 1 English

The plot of the complex number $$w = 1/z$$

A
GATE EE 2011 Engineering Mathematics - Complex Variable Question 1 English Option 1
B
GATE EE 2011 Engineering Mathematics - Complex Variable Question 1 English Option 2
C
GATE EE 2011 Engineering Mathematics - Complex Variable Question 1 English Option 3
D
GATE EE 2011 Engineering Mathematics - Complex Variable Question 1 English Option 4
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