1
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
$$i$$
2
AIEEE 2003
+4
-1
Let $${Z_1}$$ and $${Z_2}$$ be two roots of the equation $${Z^2} + aZ + b = 0$$, Z being complex. Further , assume that the origin, $${Z_1}$$ and $${Z_2}$$ form an equilateral triangle. Then
A
$${a^2} = 4b$$
B
$${a^2} = b$$
C
$${a^2} = 2b$$
D
$${a^2} = 3b$$
3
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.
4
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
$$- \omega$$
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