# 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.