Let z1, z2, z3 be three vertices of an equilateral triangle circumscribing the circle `|z| = 1/2`. If `z1 = 1/2+ ((sqrt3)iota)/2` and z1, z2, z3 are in the anticlockwise sense then z2 is

Let z1, z2, z3 be three vertices of an equilateral triangle circumscri

1.	Let z1, z2, z3 be three vertices of an equilateral triangle circumscribing the circle `\|z\| = 1/2`. If `z1 = 1/2+ ((sqrt3)iota)/2` and z1, z2, z3 are in the anticlockwise sense then z2 is
Answer» `abs(z)=1/2`,it represents circle withcircle center `(0.0)`r=1/2 by drawing figure we get,since, z_2 is anticlockwise z_1=-1/2 `z_1=1/2+sqrt(3)i/2` andArgument (z)=`sqrt(3)` `tan theta=sqrt(3)``theta=60^@``Abs(z)=sqrt((1/2)^2+(sqrt(3)/2)^2)=1`similarly`abs(z_1)=abs(z_2)=abs(z_3)` So,`abs(z)`=1and `z` lies on the real axis of the positive direction`:.` Ans=D