1
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
$$5\sqrt 2$$
2
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
$${z^9} = 1$$
3
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
4
GATE IN 1997
+1
-0.3
The complex number $$z\, = \,x\, + \,jy$$ which satisfy the equation $$\left| {z + 1} \right|\, = \,1$$ lie on
A
a circle with ( 1, 0 ) as the center and radius 1
B
a circle with ( - 1, 0 ) as the center and radius 1
C
y-axis
D
x-axis
GATE IN Subjects
Engineering Mathematics
EXAM MAP
Joint Entrance Examination