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

Here is Why You Need An Adapter

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

Cook Islands

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

Type I

Balearic Islands

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

Type C

Type F