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
$$2 - \sqrt {3,} $$ $$2 - \sqrt {3} $$
2
IIT-JEE 1988
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For any two complex numbers $${z_1},{z_2}$$ and any real number a and b.