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

Here is Why You Need An Adapter

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

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

Type I

In New Caledonia, outlets of type C and F are in use.

Type C

Type F

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