Here is how I'd answer the complex section of the exam.
I don't use complex numbers in my professional life as a mathematician. This means that every time I teach this, I have to teach myself all over again how to do complex analysis, going over my university calc notes.
This is another good reason to keep clear and concise notes--you may need to use them yourself years later!
You will use complex analysis in a range of technical fields including engineering and electrical fields.
I do use the closely related field of linear algebra all the time, and it is very likely that you'll need to use linear algebra if you go into a technical field.
Anyway, if I made a mistake please let me know.
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