If the points `A(z),B(-z),a n dC(1-z)` are the vertices of an equilateral triangle `A B C ,` then sum of possible `z` is 1/2 sum of possible `z` is 1 product of possible `z` is 1/4 product of possible `z` is

Options

A. sum of possible z is `1//2`
B. sum of possible z is
C. product of possible z is `1//4`
D. product of possibble z is `1//2`.

Answer

A, C

Explanation

Tringle ABC is equailateral. Hence,
`z^(2) + (-z)^(2) + (1-z)^(2) = z(-z) + z(1-z) + (-z) (1-z)`
or `3z^(2) - 2z + 1= z^(2)`
or `4z^(2) -2z+ 1=0`
Sum of roots `=(1)/(2)`
and Product of roots `=(1)/(4)`