If `z_r=cos(pi/3^r)+i sin(pi/3^r)` where `r in N` then `z_1.z_2.z_3...oo=`

z=(1-i)/(cos(pi/3)+i sin(pi/3))

If z_r=cos(pi/(3^r))+isin(pi/(3^r)),r=1,2,3, , prove that z_1z_2z_3 .... z_oo=i

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

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_n=[cos (pi/2)^(n/2)+i sin (pi/2)^(n/2)] then z_1.z_2.z_3…….oo

If z_(r)=cos((pi)/(3^(r)))+i sin((pi)/(3^(r))),r=1,2,3 prove that z_(1)z_(2)z_(3)z_(oo)=i

If Z_r =cos ((pi)/(2^r))+isin((pi)/(2^r)) then Z_(1).Z_(2).Z_(3)"…….." upto oo equals

If x_(r)=cos((pi)/(2^(r)))+i sin((pi)/(2^(r))),z_(t)=cos((pi)/(3^(t)))+i sin((pi)/(3^(r))) where r=1,2,3,... and t=1,2,3,..., then the value of (x_(1)x_(2)x_(3).........oo)^(2)(z_(1)z_(2)z_(3)...oo)^(4) is