Power inverters are always fairly complicated, particularly if you want good efficiency and/or high power. That's normally quite expensive. Fortunately, so many people have been mass-producing complicated inverters that the cost is quite reasonable, considering the contents.
They all involve high frequency transformers unless you have 120V DC of battery power available to switch back and forth. High freq transformer design is one of the most complicated aspects of electrical engineering unless you only want a crude (low power, low efficiency for the cost, weight, & size) result.