1
IIT-JEE 1996
Fill in the Blanks
+2
-0
The value of the expression
$$1 \bullet \left( {2 - \omega } \right)\left( {2 - {\omega ^2}} \right) + 2 \bullet \left( {3 - \omega } \right)\left( {3 - {\omega ^2}} \right) + \,....... + \left( {n - 1} \right).\left( {n - \omega } \right)\left( {n - {\omega ^2}} \right),$$

where $$\omega$$ is an imaginary cube root of unity, is..........

2
IIT-JEE 1994
Fill in the Blanks
+2
-0
Suppose Z1, Z2, Z3 are the vertices of an equilateral triangle inscribed in the circle $$\left| Z \right| = 2.$$ If Z1 = $$1 + i\sqrt 3$$ then Z2 = ......., Z3 =..............
3
IIT-JEE 1993
Fill in the Blanks
+2
-0
$$ABCD$$ is a rhombus. Its diagonals $$AC$$ and $$BD$$ intersect at the point $$M$$ and satisfy $$BD$$ = 2$$AC$$. If the points $$D$$ and $$M$$ represent the complex numbers $$1 + i$$ and $$2 - i$$ respectively, then A represents the comp[lex number ..........or..........
4
IIT-JEE 1989
Fill in the Blanks
+2
-0
If $$a,\,b,\,c,$$ are the numbers between 0 and 1 such that the ponts $${z_1} = a + i,{z_2} = 1 + bi$$ and $${z_3} = 0$$ form an equilateral triangle,
then a= .......and b=..........
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