You Do Need power plug adapter while traveling from Zimbabwe to Burundi.

Here is Why You Need An Adapter

The outlet and plug type used in Burundi are C and E and in Zimbabwe are D and G. This is how they look like.

Zimbabwe

In Zimbabwe, outlets of type D and G are in use.

Type D

Type G

Burundi

In Burundi, outlets of type C and E are in use.

Type C

Type E