If ( , ) and ( ) are angles that satisfy the following conditions, find the value of (x y z ). 1. ( ( )+ ( )+ ( ) ) (= ( ) ( ) ( ) ) 2. (x= ( )+i ( ) ) 3. (y= ( )+i ( ) ) 4. (z= ( )+i ( ) )

Step-by-step solution

It is given that, ( aligned & + + = & + =- (1- ) & + 1- = (- ) & ( + )= (- ) + =n - , n I & + + =n , n I & and x= +i , y= +i , & z= +i & x y z=e^ i . e^ i . e^ i & =e^ i( + + ) =e^ i n = n =1 or -1 & x y z= 1 aligned ) Hence, option (c) is correct.