Does it make sense to apply complex mathematics in economics given that the result can be off by substantial percentage points? Complex mathematics make sense if the results can be calculated with precision. This applies for the physical sciences like physics and engineering. Economics is more of a social science subject. Does complex mathematics make sense in this context?
In the field of economics complex math is often used for

a) Economic modelling

There are usually tons of factors that influence even the simplest economic event. It is often necessary to resort to complex math to include all the variables that represent those factors in the right way.

b) Analysis of statistical data

It is often very difficult to support economic theories with good data, again because there are so many factors in play. On top of that, many simple mathematical instruments have drawbacks and should not be applied in certain situations. For example, to test relationship between two variables, you can use a simple correlation coefficient, but there are cases where outliers or certain patterns can make it unreasonably high or low. Then you can use simple linear regression, but if you spent months gathering data you may want to spend a few days trying to build a custom regression equation for a better fit. Finally, if you are preparing a paper for publication, you may want to use as many statistics as you can to try to convince reviewers and readers that your findings are actually true.

Drawbacks of using complex math in economics

1) There are not that many readers out there who are proficient in advanced mathematics. Unless you want to limit your target audience to a few math enthusiasts, keep it as simple as possible.

2) If you are preparing a paper for review at a journal, keep in mind that reviewers in economic journals are not necessarily mathematicians. It usually takes longer for math-heavy papers to get reviewed and the quality of those reviews may not be great, unless its a top journal.