1
GATE CE 2015 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Consider the following complex function $$f\left( z \right) = {9 \over {\left( {z - 1} \right)\left( {z + 2} \right)}}.$$ Which of the following is ONE of the residues of the above function ?
A
$$-1$$
B
$${9 \over {16}}$$
C
$$2$$
D
$$9$$
2
GATE CE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
$$z = {{2 - 3i} \over { - 5 + i}}$$ can be expressed as
A
$$-0.5-0.5i$$
B
$$-0.5+0.5i$$
C
$$0.5-0.5i$$
D
$$0.5+0.5i$$
3
GATE CE 2011
MCQ (Single Correct Answer)
+1
-0.3
For an analytic function $$f\left( {x + i\,y} \right) = u\left( {x,y} \right) + i\,v\left( {x,y} \right),\,u$$ is given by $$u = 3{x^2} - 3{y^2}.$$ The expression for $$v,$$ considering $$k$$ is to be constant is
A
$$3{y^2} - 3{x^2} + k$$
B
$$6x - 6y + k$$
C
$$6y - 6x + k$$
D
$$6xy + k$$
4
GATE CE 2010
MCQ (Single Correct Answer)
+1
-0.3
The modulus of the complex number $${{3 + 4\,i} \over {1 - 2\,i}}$$ is
A
$$5$$
B
$$\sqrt 5 $$
C
$${1 \over {\sqrt 5 }}$$
D
$${1 \over 5}$$
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