1
IIT-JEE 2000 Screening
+2
-0.5
If $${z_1},\,{z_2}$$ and $${z_3}$$ are complex numbers such that $$\left| {{z_1}} \right| = \left| {{z_2}} \right| = \left| {{z_3}} \right| = \left| {{1 \over {{z_1}}} + {1 \over {{z_2}}} + {1 \over {{z_3}}}} \right| = 1,$$ then $$\left| {{z_1} + {z_2} + {z_3}} \right|$$ is
A
equal to 1
B
less than 1
C
greater than 3
D
equal to 3
2
IIT-JEE 2000 Screening
+2
-0.5
If $$\arg \left( z \right) < 0,$$ then $$\arg \left( { - z} \right) - \arg \left( z \right) =$$
A
$$\pi$$
B
$$- \pi$$
C
$$- {\pi \over 2}$$
D
$${\pi \over 2}$$
3
IIT-JEE 1999
+2
-0.5
$$If\,i = \sqrt { - 1} ,\,\,then\,\,4 + 5{\left( { - {1 \over 2} + {{i\sqrt 3 } \over 2}} \right)^{334}} + 3{\left( { - {1 \over 2} + {{i\sqrt 3 } \over 2}} \right)^{365}}$$ is equal to
A
$$1 - i\sqrt 3$$
B
$$- 1 + i\sqrt 3$$
C
$$i\sqrt 3$$
D
$$- i\sqrt 3$$
4
IIT-JEE 1996
+1
-0.25
For positive integers $${n_1},\,{n_2}$$ the value of the expression $${\left( {1 + i} \right)^{^{{n_1}}}} + {\left( {1 + {i^3}} \right)^{{n_1}}} + {\left( {1 + {i^5}} \right)^{{n_2}}} + {\left( {1 + {i^7}} \right)^{{n_2}}},$$
where $$i = \sqrt { - 1}$$ is real number if and only if
A
$${n_1} = {n_2} + 1$$
B
$${n_1} = {n_2} - 1$$
C
$${n_1} = {n_2}$$
D
$${n_1} > 0,\,{n_2} > 0$$
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