Home
Class 12
MATHS
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,...,n and i=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))`

Text Solution

Verified by Experts

Promotional Banner

Similar Questions

Explore conceptually related problems

lim_(n rarr oo) (1+2+3+…...+n)/(n^(2)), n in N is equal to :

lim_(n to oo) 1/(n^2) sum_(r = 1)^(n) re^(r//n) equals :

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

lim_(n to oo) sum_(r = 1)^(n) 1/n sin(r pi)/(2pi) is :

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

lim_(n rarr oo) 1/2 [(n+1)(n+2)…….2n]^(1/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

lim_(n rarr oo) (1)/(n^(3)) sum_(r = 1)^(n) r^(2) is :

If f(z)=(7-z)/(1-z^(2)), where z=1+2 i, then |f(z)| is