You Do Need power plug adapter while traveling from Norfolk Island 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 Norfolk Island is I. This is how they look like.

Norfolk Island

In Norfolk Island, 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