1
AIEEE 2004
+4
-1
Let z and w be complex numbers such that $$\overline z + i\overline w = 0$$ and arg zw = $$\pi$$. Then arg z equals
A
$${{5\pi } \over 4}$$
B
$${{\pi } \over 2}$$
C
$${{3\pi } \over 4}$$
D
$${{\pi } \over 4}$$
2
AIEEE 2004
+4
-1
If $$z = x - iy$$ and $${z^{{1 \over 3}}} = p + iq$$, then

$${{\left( {{x \over p} + {y \over q}} \right)} \over {\left( {{p^2} + {q^2}} \right)}}$$ is equal to
A
- 2
B
- 1
C
2
D
1
3
AIEEE 2004
+4
-1
If $$\,\left| {{z^2} - 1} \right| = {\left| z \right|^2} + 1$$, then z lies on
A
an ellipse
B
the imaginary axis
C
a circle
D
the real axis
4
AIEEE 2003
+4
-1
If $$z$$ and $$\omega$$ are two non-zero complex numbers such that $$\left| {z\omega } \right| = 1$$ and $$Arg(z) - Arg(\omega ) = {\pi \over 2},$$ then $$\,\overline {z\,} \omega$$ is equal to
A
$$- i$$
B
1
C
- 1
D
$$i$$
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