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 (-1)^(1/3) = -1.
It rather depends on the context.

-1 has three cube roots:

-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.