You cannot INSERT INTO vwMyCompexView
using T-SQL, nor can you use SQL Management Studio's grid GUI to insert data into a view that is composed of an underlying join.
You CAN use the SQL Mgmt Studio grid GUI or T-SQL to insert data into a view that is composed of a single table, that DOESN'T perform any computations or aggregate functions. Only those views who are a straight mirror of the base table can be inserted to. If your view excludes a column that is non-nullable and has no default value, the insert would fail.
My recommendation would be to always script your inserts by using stored procedures. (I actually had to TRY those two scenarios before answering this question. I'd never considered using a view to insert data. That's just me; YMMV.)