1
IIT-JEE 2006
+3
-0.75
If $${{w - \overline w z} \over {1 - z}}$$ is purely real where $$w = \alpha + i\beta ,$$ $$\beta \ne 0$$ and $$z \ne 1,$$ then the set of the values of z is
A
$$\left\{ {z:\left| z \right| = 1} \right\}$$
B
$$\left\{ {z:z = \overline z } \right\}$$
C
$$\left\{ {z:z \ne 1} \right\}\,\,$$
D
$$\left\{ {z:\left| z \right| = 1,z \ne 1} \right\}$$
2
IIT-JEE 2005 Screening
+2
-0.5
$$a,\,b,\,c$$ are integers, not all simultaneously equal and $$\omega$$ is cube root of unity $$\left( {\omega \ne 1} \right),$$ then minimum value of $$\left| {a + b\omega + c{\omega ^2}} \right|$$ is
A
0
B
1
C
$${{\sqrt 3 } \over 2}$$
D
$${1 \over 2}$$
3
IIT-JEE 2004 Screening
+2
-0.5
If $$\omega$$ $$\left( { \ne 1} \right)$$ be a cube root of unity and $${\left( {1 + {\omega ^2}} \right)^n} = {\left( {1 + {\omega ^4}} \right)^n},$$ then the least positive value of n is
A
2
B
3
C
5
D
6
4
IIT-JEE 2003 Screening
+2
-0.5
If $$\,\left| z \right| = 1$$ and $$\omega = {{z - 1} \over {z + 1}}$$ (where $$z \ne - 1$$), then $${\mathop{\rm Re}\nolimits} \left( \omega \right)$$ is
A
0
B
$$- {1 \over {{{\left| {z + 1} \right|}^2}}}$$
C
$$\left| {{z \over {z + 1}}} \right|.{1 \over {{{\left| {z + 1} \right|}^2}}}$$
D
$$\,{{\sqrt 2 } \over {{{\left| {z + 1} \right|}^2}}}$$
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