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`a` and `b` are real numbers between 0 and 1 such that the points `z_1 =a+ i`, `z_2=1+ bi`, `z3= 0` form an equilateral triangle, then `a` and `b` are equal to

A

`a = b = 2 - sqrt(3)`

B

`a = 2 - sqrt(3), b = sqrt(3) - 1`

C

`a = sqrt(3) - 1, b = 2 - sqrt(3)`

D

None of these

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A
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