If x_n= 2^n +i 2^n , then _ n=1 ^ x_n is equal to

Step-by-step solution

aligned & Given that, = 9+6 i 13 & aligned X_n & = 2^n +i 2^n = cis 2^n _ n=1 ^ X_n & = _ n=1 ^ cis 2^n & = cis 2 cis 2^2 cis 2^3 . & = cis ( 2 + 2^2 + 2^3 + . . ) & = cis ( 2 1- 1 2 )= cis & =-1 aligned aligned