1

IIT-JEE 1996

MCQ (Single Correct Answer)
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
$${n_1} > 0,\,{n_2} > 0$$
2

IIT-JEE 1995 Screening

MCQ (Single Correct Answer)
Let $$z$$ and $$\omega $$ be two non zero complex numbers such that
$$\left| z \right| = \left| \omega \right|$$ and $${\rm A}rg\,z + {\rm A}rg\,\omega = \pi ,$$ then $$z$$ equals
A
$$\omega $$
B
$$ - \omega $$
C
$$\overline \omega $$
D
$$ - \overline \omega $$
3

IIT-JEE 1995 Screening

MCQ (Single Correct Answer)
Let $$z$$ and $$\omega $$ be two complex numbers such that
$$\left| z \right| \le 1,$$ $$\left| \omega \right| \le 1$$ and $$\left| {z + i\omega } \right| = \left| {z - i\overline \omega } \right| = 2$$ then $$z$$ equals
A
$$1$$ or $$i$$
B
$$i$$ or $$-i$$
C
$$1$$ or $$ - 1$$
D
$$i$$ or $$ - 1$$
4

IIT-JEE 1995 Screening

MCQ (Single Correct Answer)
If $$\omega \,\left( { \ne 1} \right)$$ is a cube root of unity and $${\left( {1 + \omega } \right)^7} = A + B\,\omega $$ then $$A$$ and $$B$$ are respectively
A
0, 1
B
1, 1
C
1, 0
D
-1, 1

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