1
WB JEE 2008
+1
-0.25

For two complex numbers z1, z2 the relation $$\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|$$ holds if

A
$$\arg ({z_1}) = \arg ({z_2})$$
B
$$\arg ({z_1}) + \arg ({z_2}) = {\pi \over 2}$$
C
$${z_1}{z_2} = 1$$
D
$$\left| {{z_1}} \right| = \left| {{z_2}} \right|$$
2
WB JEE 2008
+1
-0.25

If 1, $$\omega$$, $$\omega$$2 are cube roots of unity, then $$\left| {\matrix{ 1 & {{\omega ^n}} & {{\omega ^{2n}}} \cr {{\omega ^{2n}}} & 1 & {{\omega ^n}} \cr {{\omega ^n}} & {{\omega ^{2n}}} & 1 \cr } } \right|$$ has value

A
0
B
$$\omega$$
C
$$\omega$$2
D
$$\omega$$ + $$\omega$$2
3
WB JEE 2009
+1
-0.25

If $$i = \sqrt { - 1}$$ and n is positive integer, then $${i^n} + {i^{n + 1}} + {i^{n + 2}} + {i^{n + 3}}$$ is equal to

A
1
B
i
C
in
D
0
4
WB JEE 2009
+1
-0.25

The modulus of $${{1 - i} \over {3 + i}} + {{4i} \over 5}$$ is

A
$$\sqrt 5$$ unit
B
$${{\sqrt {11} } \over 5}$$ unit
C
$${{\sqrt 5 } \over 5}$$ unit
D
$${{\sqrt {12} } \over 5}$$ unit
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