1
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
$${z^9} = 1$$
2
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
3
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
4
GATE IN 1994
+1
-0.3
The real part of the complex number $$z\, = \,x\, + \,iy$$ is given by
A
$${\mathop{\rm Re}\nolimits} (z)\, = \,z\, - \,{z^*}$$
B
$${\mathop{\rm Re}\nolimits} (z)\, = \,{{z\, - \,{z^*}} \over 2}$$
C
$${\mathop{\rm Re}\nolimits} (z)\, = \,{{z\, + \,{z^*}} \over 2}$$
D
$${\mathop{\rm Re}\nolimits} (z)\, = \,z\, + \,{z^*}$$
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