The smallest positive integral value of `'n'` such that `[(1+sin\ pi/8 + i\ cos\ pi/8)/(1+sin\ pi/8 - i\ cos\ pi/8)]^n` is purely imaginary if

The smallest positive integral value of ' n ' such that [(1+sin (pi)/(8)+i cos (pi)/(8))(1+sin (pi)/(8)-i cos (pi)/(8))]^(n) is purely imaginary is

The smallest positive integral value of n such that [(1+"sin"pi/8+i"cos"(pi)/8)/(1+"sin"(pi)/8-i"cos"(pi)/8)]^(n) is purely imaginary is n=

((sin (pi/8)+i cos (pi/8))/(sin (pi/8)-i cos (pi/8)))^(8)=

The smallest positive integral value of ‘n’ such that [(1+sin frac (pi)(8)+i cos frac (pi)(8))/(1+sin frac (pi)(8)-i cos frac (pi)(8))]^n is purely imaginary is n =

[(1+sin(pi//8)+icos(pi//8))/(1+sin(pi//8)-icospi//8)]^(-8//3)

Show that one value of ((1 + sin . pi/8 + i cos . pi/8)/(1 + sin . pi/8 - i cos . pi/8))^(8//3) " is " - 1 .

The expression [(1+sin(pi/8)+icos(pi/8))/(1+sin(pi/8)-icos(pi/8))]^8 is equal is

((1+cos. pi/8+isin. pi/8)/(1+cos. pi/8- isin. pi/8))^(8)=

Show that one value of ((1+sin""pi/8+i cos ""pi/8)/(1+sin"" pi/8-i cos"" pi/8))^(8/3)=-1