1
AIEEE 2003
+4
-1
If $${\left( {{{1 + i} \over {1 - i}}} \right)^x} = 1$$ then :
A
x = 2n + 1, where n is any positive integer
B
x = 4n , where n is any positive integer
C
x = 2n, where n is any positive integer
D
x = 4n + 1, where n is any positive integer.
2
AIEEE 2002
+4
-1
z and w are two nonzero complex numbers such that $$\,\left| z \right| = \left| w \right|$$ and Arg z + Arg w =$$\pi$$ then z equals
A
$$\overline \omega$$
B
$$- \overline \omega$$
C
$$\omega$$
D
$$- \omega$$
3
AIEEE 2002
+4
-1
If $$\left| {z - 4} \right| < \left| {z - 2} \right|$$, its solution is given by :
A
$${\mathop{\rm Re}\nolimits} (z) > 0$$
B
$${\mathop{\rm Re}\nolimits} (z) < 0$$
C
$${\mathop{\rm Re}\nolimits} (z) > 3$$
D
$${\mathop{\rm Re}\nolimits} (z) > 2$$
4
AIEEE 2002
+4
-1
The locus of the centre of a circle which touches the circle $$\left| {z - {z_1}} \right| = a$$ and$$\left| {z - {z_2}} \right| = b\,$$ externally

($$z,\,{z_1}\,\& \,{z_2}\,$$ are complex numbers) will be :
A
an ellipse
B
a hyperbola
C
a circle
D
none of these
EXAM MAP
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