How do you simplify #(-1)^(1/3)#?
1 Answer
Jan 7, 2016
It depends.
Explanation:
In Real arithmetic you don't have any choice:
#(-1)^(1/3) = -1#
In Complex arithmetic you might prefer to define:
#(-1)^(1/3) = cos(pi/3) + i sin(pi/3) = 1/2 + sqrt(3)/2 i#
or you might prefer to stick with
It rather depends on the context.
#-1#
#1/2+sqrt(3)/2 i#
#1/2-sqrt(3)/2 i#
If you are dealing with Complex arithmetic then you commonly want to be aware of all three.