four points z1, z2, z3, z4, in complex plane such that |z1| < 1, |z3| = 1, |z2| <= 1 and z2 =z3(z1-z4)/(z1'z4 -1) then |z4| can be (1) 1/2 (2) 2/3 (3) 3/2 (4) 5/4

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If | $z_{1} | = | z_{2} | = | z_{3} | = | z_{4} | = 1$ and $z_{1} + z_{2} + z_{3} + z_{4} = 0$
then least value of the expression
$E = | z_{1} - z_{2} |^{2} + | z_{2} - z_{3} |^{2} + | z_{3} - z_{4} |^{2} + | z_{4} - z_{1} |^{2}$ is

Q. If

| z_{1} | = | z_{2} | = | z_{3} | = | z_{4} | = 1

and

z_{1} + z_{2} + z_{3} + z_{4} = 0

, then least value of the expression

E = | z_{1} - z_{2} |^{2} + | z_{2} - z_{3} |^{2} + | z_{3} - z_{4} |^{2} + | z_{4} - z_{1} |^{2}

Q. If

| z_{1} | = | z_{2} | = | z_{3} | = | z_{4} |

and

z_{1} + z_{2} + z_{3} + z_{4} = 0

then the points

z_{1}, z_{2}, z_{3}, z_{4}

in the Argand plane are the vertices of a

Q. If

z_{1} + z_{2} + z_{3} + z_{4} = 0

, then the expression

| z_{1} - z_{2} |^{2} + | z_{2} - z_{3} |^{2} + | z_{3} - z_{4} |^{2} + | z_{4} - z_{1} |^{2} - 2 (| z_{1} |^{2} + | z_{2} |^{2} + | z_{3} |^{2} + | z_{4} |^{2})

is equal to

0

, is and only if,

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