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1

### IIT-JEE 2000 Screening

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 1999

$$If\,i = \sqrt { - 1} ,\,\,then\,\,4 + 5{\left( { - {1 \over 2} + {{i\sqrt 3 } \over 2}} \right)^{334}} + 3{\left( { - {1 \over 2} + {{i\sqrt 3 } \over 2}} \right)^{365}}$$ is equal to
A
$$1 - i\sqrt 3$$
B
$$- 1 + i\sqrt 3$$
C
$$i\sqrt 3$$
D
$$- i\sqrt 3$$
3

### IIT-JEE 1996

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
$${n_1} > 0,\,{n_2} > 0$$
4

### IIT-JEE 1995 Screening

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
$$- \overline \omega$$

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NEET

Class 12