Round 8: Tossup 12

When evaluated over this set, functions like the logarithm are multi-valued and can be studied using branch cuts and points. Holomorphism is a generalization of differentiability for functions valued over these numbers (15[1])and is studied in a field of “analysis” named for these numbers. De Moivre’s (“duh mwah-vruh’s”) formula gives (15[1])a simple way to raise numbers in this set to the nth power. The (*) roots of unity are examples of these numbers that form a regular polygon. (-5[1])The unit circle is a way of visualizing this type of number, which can be written as “r times cosine theta plus i times sine theta.” For 10 points, name these numbers that have a real and an imaginary (10[1])part. ■END■ (10[1])

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