Let `z_(1),z_(2),z_(3),z_(4),z_(5)` and `z_(6)` are complex numbers lying on a unit circle with centre `(0,0)`. If `omega=(sum_(k=1)^(6)z_(k))(sum_(k=1)^(6)(1)/(z_(k))),` then

Let z_(1)z_(2),z_(3)...z_(n) be the complex numbers such that |z_(1)|=|z_(2)|...|z_(n)|=1. If z=(sum_(k=1)^(n)z_(k))(sum_(k=1)^(n)(1)/(z_(k))) then proves that z is a real number 0

Let z_(1),z_(2)..........z_(n) be equi-modular non-zero complex numbers such that z_(1)+z_(2)+z_(3)+...+z_(n)=0 Then Re(sum_(j=1)^(n)sum_(k=1)^(n)((z_(j))/(z_(k))))

If z_(1) and z_(2) are two complex numbers then prove that |z_(1)-z_(2)|^(2)<=(1+k)z_(1)^(2)+(1+(1)/(k))z_(2)^(2)

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

Let z_(1),z_(2),z_(3),z_(4) are distinct complex numbers satisfying |z|=1 and 4z_(3) = 3(z_(1) + z_(2)) , then |z_(1) - z_(2)| is equal to

If z_(1),z_(2),z_(3),…………..,z_(n) are n nth roots of unity, then for k=1,2,,………,n

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

Show that if z_(1)z_(2)+z_(3)z_(4)=0 and z_(1)+z_(2)=0 ,then the complex numbers z_(1),z_(2),z_(3),z_(4) are concyclic.

Complex numbers z_(1),z_(2),z_(3) are the vertices A,B,C respectively of an isosceles right angled trianglewith right angle at C and (z_(1)-z_(2))^(2)=k(z_(1)-z_(3))(z_(3)-z_(2)) then find k.