1
GATE IN 2007
+1
-0.3
For the function $${{\sin z} \over {{z^3}}}$$ of a complex variable z, the point z = 0 is
A
a pole of order 3
B
a pole of order 2
C
a pole of order 1
D
not a singularity
2
GATE IN 2005
+1
-0.3
Consider the circle $$\left| {z\, - 5\, - 5i} \right|\, = \,2$$ in the complex number plane (x, y) with z = x + iy. The minimum distance from the origin to the circle is
A
$$5\sqrt 2 - 2$$
B
$$\sqrt {54}$$
C
$$\sqrt {34}$$
D
$$5\sqrt 2$$
3
GATE IN 2005
+1
-0.3
Let $${z^3}\, = \,\overline z$$, where z is a complex number not equal to zero. Then z is a solution of
A
$${z^2} = 1$$
B
$${z^3} = 1$$
C
$${z^4} = 1$$
D
$${z^9} = 1$$
4
GATE IN 2002
+1
-0.3
The bilinear transformation $$w\, = \,{{z\, - \,1} \over {z\, + \,1}}$$
A
maps the inside of the unit circle in the z-plane to left half of the w - plane
B
maps the outside of the unit circle in the z-plane to left half of the w - plane
C
maps the inside of the unit circle in the z-plane to right half of the w - plane
D
maps the outside of the unit circle in the z-plane to right half of the w - plane
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