1

### IIT-JEE 1981

The complex numbers $$z = x + iy$$ which satisfy the equation $$\,\left| {{{z - 5i} \over {z + 5i}}} \right| = 1$$ lie on
A
the x-axis
B
the straight line y=5
C
a circle passing through the origin
D
none of these
2

### IIT-JEE 1980

The smallest positive integer n for which $${\left( {{{1 + i} \over {1 - i}}} \right)^n} = 1$$ is
A
$$n = 8$$
B
$$n = 16$$
C
$$n = 12$$
D
none of these
3

### IIT-JEE 1979

If the cube roots of unity are $$1,\,\omega ,\,{\omega ^2},$$ then the roots of the equation $${\left( {x - 1} \right)^3} + 8 = 0$$ are
A
$$- 1,1 + 2\omega ,\,1 + 2{\omega ^2}$$
B
$$- 1,1 - 2\omega ,\,1 - 2{\omega ^2}$$
C
$$- 1, - 1, - 1$$
D
None of these

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