If z(r)=cos((ralpha)/(n^(2)))+isin((ralp...

If `z_(r)=cos((ralpha)/(n^(2)))+isin((ralpha)/(n^(2))),"where"r=1,2,3,...,nandi=sqrt(-1),"then"lim_(n to oo) z_(1)z_(2)z_(3)...z_(n)` is equal to

A

`e^(ialpha)`

B

`e^(-ialpha//2)`

C

`e^(ialpha//2)`

D

`root3(e^(ialpha))`

Verified by Experts

Similar Questions

Explore conceptually related problems

If z=cos((pi)/(3))-isin((pi)/(3)) then z^(2)-z+1=....

lim_(n -> oo) (((n+1)(n+2)(n+3).......3n) / n^(2n))^(1/n) is equal to

|z_(1)+z_(2)|=|z_(1)|+|z_(2)| is possible, if

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=ilog_(e)(2-sqrt(3)),"where"i=sqrt(-1) then the cos z is equal to

z_(1)=3+I and z_(2)=-2+6i then find z_(1)z_(2)

z_(1)=9+3i and z_(2)=-2-i then find z_(1)-z_(2)

If z=(sqrt(3)-i)/2 , where i=sqrt(-1) , then (i^(101)+z^(101))^(103) equals to

z_(1)=9+3i and z_(2)=-2-i" then find "(z_(1))/(z_(2))

The value of the lim_(n->oo)tan{sum_(r=1)^ntan^(- 1)(1/(2r^2))} is equal to