$$ABCD$$ 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 $$1 - {3 \over 2}i$$
2
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
$$2 - \sqrt {3,} $$ $$2 - \sqrt {3} $$
3
IIT-JEE 1988
Fill in the Blanks
For any two complex numbers $${z_1},{z_2}$$ and any real number a and b.