[" (11) If "|z-1|+|z+3|<=8" ,then the range of "],[" of "|z-4|" is "]

The minimum value of |z-1|+|z-3| is

Let z_(1), z_(2), z_(3) be three complex numbers such that |z_(1)| = |z_(2)| = |z_(3)| = 1 and z = (z_(1) + z_(2) + z_(3))((1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))) , then |z| cannot exceed

If |z-1|=|z-3| then the locus of z is

z_(1), z_(3), and z_(3) are complex numbers such that z_(1) + z_(2) + z_(3)=0 and |z_(1)| = |z_(2)| = |z_(3)| = 1 then z_(1)^(2)+z_(2)^(2)+z_(3)^(3)

If complex numbers z_(1)z_(2) and z_(3) are such that |z_(1)| = |z_(2)| = |z_(3)| , then prove that arg((z_(2))/(z_(1)) = arg ((z_(2) - z_(3))/(z_(1) - z_(3)))^(2)