1

### IIT-JEE 2007

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
$$\left( {3 + 4i} \right){e^{i\pi /4}}$$
2

### IIT-JEE 2006

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
$$\left\{ {z:\left| z \right| = 1,z \ne 1} \right\}$$
3

### IIT-JEE 2005 Screening

$$a,\,b,\,c$$ 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
$${1 \over 2}$$
4

### IIT-JEE 2004 Screening

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

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