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

Here is Why You Need An Adapter

The outlet and plug type used in Cyprus is G 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

Cyprus

In Cyprus, outlets of type G are in use.

Type G