सम्मिश्र तल में सम्मिश्र संख्या z द्वारा प्रदर्शित बिन्दुओं को दर्शाइये :|(z-3)/(z+3)| = 3 | 12 ...

z is such that arg((z-3sqrt(3))/(z+3sqrt(3)))=(pi)/(3) then locus z is

(x + y) ^ (3) + (y + z) ^ (3) + (z + x) ^ (3) -3 (x + y) (y + z) (z + x)

If z_(1) + z_(2) + z_(3) = 0 and |z_(1)| = |z_(2)| = |z_(3)| = 1 , then value of z_(1)^(2) + z_(2)^(2) + z_(3)^(2) equals

If | z_ (1) | = | z_ (2) | = | z_ (3) | = 1 & z_ (1) + z_ (2) + z_ (3) = sqrt (2) + i then ((z_ (1) ) / (z_ (2)) + (z_ (2)) / (z_ (3)) + (z_ (3)) / (z_ (4))) =

If | z_ (1) | = | z_ (2) | = | z_ (3) | = 1 & z_ (1) + z_ (2) + z_ (3) = sqrt (2) + i then ((z_ (1) ) / (z_ (2)) + (z_ (2)) / (z_ (3)) + (z_ (3)) / (z_ (4))) =