What is the uses of complex fertilizer?

If you were growing plants (lettuce etc) in a completely aquatic environment, (hydroponics) then your fertilizer mix would have to contain the quite wide range of minerals essential for plant growth.

Another more common need for a more complex fertilizer would be if the local area soils were deficient in a particular mineral. In New Zealand, much of the volcanic soils are deficient in Selenium, and it needs be applied both for the health of the grass, and of the animals that graze on it.