[" 89.If "z_(r)=cos((pi)/(2^(r)))+i sin((dot pi)/(2^(r)))," find the value of "z_(1)*z_(2)],[z_(3)..." to "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))) + i sin ((pi )/( 2 ^(r))), then z _(1) . z _(2). z _(3)... upto oo equals : a)-3 b)-2 c)-1 d)0

If z_(n)=cos((pi)/((2n+1)(2n+3)))+i sin((pi)/((2n+1)(2n+3))) ,then lim_(n rarr oo)(z_(1)*z_(2)*z_(3)...z_(n))=

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

If arg((z_(1))/(z_(2)))=(pi)/(2), then find the value of |(z_(1)+z_(2))/(z_(1)-z_(2))|

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

If z_(k)=cos((k pi)/(10))+i sin((k pi)/(10)), then z_(1)z_(2)z_(3)z_(4) is equal to (A)-1 (B) 2(C)-2 (D) 1