MATH 388 Worksheet on Fields

1. a) Fill in the operation tables for .

+	0	1	2	3	4	5	6	7	8	9	10
0
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10

	0	1	2	3	4	5	6	7	8	9	10
0
1
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10

b) Find a generator of .

2. In the field find and .

3. In the field, , of complex numbers, write each of the following in the form a + bi where a and b are real numbers:

a) b) c) d)

4. Let . Evaluate f(1), f(2), and f(3) in

5. Find a non-zero polynomial, f(x), such that f(a) = 0 for all a in