You Do Need power plug adapter while traveling from Balearic Islands to Cook Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Cook Islands is I and in Balearic Islands are C and F. This is how they look like.

Balearic Islands

In Balearic Islands, outlets of type C and F are in use.

Type C

Type F

Cook Islands

In Cook Islands, outlets of type I are in use.

Type I