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The main things that I will look for is that each paper should have a clearly stated goal, precise statements of the key results, a few worked out examples, and at least one complete mathematical proof.
Some topics that you might consider include
– Arithmetic properties of complex numbers, construction of nth roots of unity, and a short discussion of the Fundamental Theorem of Algebra
– Arithmetic properties of the ring Z[i] of Gaussian integers, including a discussion of the analogue of the Division Algorithm in this ring
– A discussion of the method for finding roots of degree 3 (or cubic) equations via explicit formulas — the formulas are similar in spirit to the quadratic formula for degree 2 equations, but are quite a bit more complicated.
You can choose other topics,
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