Share more details. What is your datasource? How do you store "Assigned" person's name etc.
If you are using sharepoint. And Assigned is person type colum and task completed is choice type column.
Your trigger will be
When item is created or modified in SharePoint
Then condition block.
2 conditions in AND block
1.Assigned equal to 'Hardcode your email id'
2.Status equal to Completed
In the YES block of condition. Send email.
In the NO block. Nothing
