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

Here is Why You Need An Adapter

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

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

Type C

Type F

In New Zealand, outlets of type I are in use.

Type I

I am from

going to