Simplify: `[(1+sin pi/8+i cos pi/8)/(1+sin pi/8-i cos pi/8)]^(1/2)`

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

[(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 .

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

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

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

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=

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)=

The expression [(1+sin((pi)/(8))+i cos((pi)/(8)))/(1+sin((pi)/(8))-i cos((pi)/(8)))]^(8)