If `z_r=cos(pi/(3_r))+isin(pi/(3_r)),r=1,2,3, ,` prove that `z_1z_2z_3 z_oo=idot`

If z_(r)=cos.(2rpi)/(5)+isin.(2rpi)/(5) , r=0,1,2,3,4 , then z_(1)z_(2)z_(3)z_(4)z_(5) equals

If x_(r)=cos. (pi)/(2^(r))+ isin. (pi)/(2^(r)) , then x_(1)x_(2)x_(3)....oo=

If z_(k)=cos.(pi)/(2^(k))+isin.(pi)/(2^(k)) , k=1,2............ , then the value of z_(1)z_(2) ...............to oo is

If z_(1),z_(2),z_(3) are complex numbers such that : |z_(1)|=|z_(2)|=|z_(3)|=|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 , then |z_(1)+z_(2)+z_(3)| is equal to

If theta_(i)in[0,pi//6],i=1,2,3,4,5,and sintheta_(1)z^(4)+sin theta_(2)z^(3)+sintheta_(3)z^(2)+sintheta_(4)z+sintheta_(5)=2, show that (3)/(4)lt|Z|lt1.

If |z_(1)| = 1, |z_(2)| =2, |z_(3)|=3, and |9z_(1)z_(2) + 4z_(1)z_(3)+ z_(2)z_(3)|= 12 , then find the value of |z_(1) + z_(2) + z_(3)| .

If |z_(1)|=|z_(2)|=|z_(3)|=1 and z_(1)+z_(2)+z_(3)=0 , then z_(1),z_(2),z_(3) are vertices of

Let omega be the complex number cos (2 pi)/(3)+i sin (2 pi)/(3) . Then the number of distinct complex number z satisfying [[z+1,omega,omega^(2)],[omega,z+omega^2,1],[omega^(2),1,z+omega]] = 0 is equal to

For any two complex numbers z_(1) and z_(2) , prove that Re ( z_(1)z_(2)) = Re z_(1) Re z_(2)- 1mz_(1) Imz_(2)