1
IIT-JEE 2008 Paper 1 Offline
+3
-1
Let A, B, C be three sets of complex numbers as defined below

$$A = \left\{ {z:\,{\mathop{\rm Im}\nolimits} \,\,z\,\, \ge \,1} \right\}$$

$$B = \left\{ {z:\,\,\left| {z - 2 - i} \right| = 3} \right\}$$

$$C = \left\{ {z:\,{\mathop{\rm Re}\nolimits} (1 - i)z) = \sqrt 2 \,} \right\}$$

Let z be any point $$A \cap B \cap C$$ and let w be any point satisfying $$\left| {w - 2 - i} \right| < 3\,$$. Then, $$\left| z \right| - \left| w \right| + 3$$ lies between :

A
- 6 and 3
B
- 3 and 6
C
- 6 and 6
D
- 3 and 9
2
IIT-JEE 2008 Paper 1 Offline
+3
-1
Let A, B, C be three sets of complex numbers as defined below :

$$A = \left\{ {z:\,{\mathop{\rm Im}\nolimits} \,\,z\,\, \ge \,1} \right\}$$

$$B = \left\{ {z:\,\,\left| {z - 2 - i} \right| = 3} \right\}$$

$$C = \left\{ {z:\,{\mathop{\rm Re}\nolimits} (1 - i)z) = \sqrt 2 \,} \right\}$$

Let z be any point in $$A \cap B \cap C$$

Then, $${\left| {z + 1 - i} \right|^2} + {\left| {z - 5 - i} \right|^2}$$ lies between :

A
25 and 29
B
30 and 34
C
35 and 39
D
40 and 44
3
IIT-JEE 2007
+3
-0.75
A man walks a distance of 3 units from the origin towards the north-east ($$N\,{45^ \circ E }$$) direction. From there, he walks a distance of 4 units towards the north-west $$\left( {N\,{{45}^ \circ }\,W} \right)$$ direction to reach a point P. Then the position of P in the Argand plane is
A
$$3{e^{i\pi /4}} + 4i$$
B
$$\left( {3 - 4i} \right){e^{i\pi /4}}$$
C
$$\left( {4 + 3i} \right){e^{i\pi /4}}$$
D
$$\left( {3 + 4i} \right){e^{i\pi /4}}$$
4
IIT-JEE 2007
+3
-0.75
If $$\left| z \right|\, =1\,and\,z\, \ne \, \pm \,1,$$ then all the values of $${z \over {1 - {z^2}}}$$ lie on
A
a line not passing through the origin
B
$$\left| z \right|\, = \,\sqrt 2$$
C
the x-axis
D
the y-axis
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