" (vi) "(z+2)^(3)=z^(3)-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))) =

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 = e ^( 2pi l 3) , then 1 + z + 3z ^(2) + 2z ^(3) + 2z ^(4) + 3z ^(5) is equal to

If the polynomials az^(3)+4z^(2)+3z-4 and z^(3)-4z+a leave the same remainder when divided by z-3, find the value of a.

If z_(1),z_(2),z_(3) are 3 distinct complex numbers such that (3)/(|z_(2)-z_(3)|)-(4)/(|z_(3)-z_(1)|)=(5)/(|z_(1)-z_(2)|)(9)/(z_(2)-z_(3))+(16)/(z_(3)-z_(1))+(25)/(z_(1)-z_(2)) equals

The point z_(1),z_(2),z_(3),z_(4) in the complex plane are the vertices of a parallogram taken in order, if and only if. (1) z _(1) +z_(4)=z_(2)+z_(3) (2) z_(1)+z_(3) =z_(2) +z_(4) (3) z_(1)+z_(2) =z_(3)+z_(4) (4) z_(1) + z_(3) ne z_(2) +z_(4)

If z_(1),z_(2),z_(3),z_(4), are the non-real complex fifth roots of unity,then the sum of coefficient in the expansion of (3+z_(1)x+z_(2)x^(2)+z_(3)x^(3)+z_(4)x^(4))^(5) is

Let fourth roots of unity be z_(1),z_(2),z_(3) and z_(4) respectively. Statement - I: z_(1)^(2)+z_(2)^(2)+z_(3)^(2)+z_(4)^(2)=0 Statement - II: z_(1)+z_(2)+z_(3)+z_(4)=0

Let four points z_(1),z_(2),z_(3),z_(4) be in complex plane such that |z_(2)|= 1, |z_(1)|leq 1 and |z_(3)| le 1 . If z_(3) = (z_(2)(z_(1)-z_(4)))/(barz_(1)z_(4)-1) , then |z_(4)| can be

If |z_(1)|=2,|z_(2)|=3,|z_(3)|=4and|z_(1)+z_(3)+z_(3)|=2 ,then the value of |4z_(2)z_(3)+9z_(3)z_(1)+16z_(1)z_(2)|