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 =..............
Answer
$$ - 2,\,\,1 - i\sqrt 3 $$
3
IIT-JEE 1993
Fill in the Blanks
$$ABCD$$ 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..........
Answer
$$3 - {i \over 2}$$ or $$1 - {3 \over 2}i$$
4
IIT-JEE 1989
Fill in the Blanks
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=..........
Answer
$$2 - \sqrt {3,} $$ $$2 - \sqrt {3} $$
Questions Asked from Complex Numbers
On those following papers in Fill in the Blanks
Number in Brackets after Paper Indicates No. of Questions