Homework 7

Write in the standard form (a+bi where a and b are real numbers):

• -(5-2i)
• 1/(5+2i)

Prove:

• every complex number has an additive inverse
• every non-zero complex number has a multiplicative inverse

Let C denote the set of complex numbers, with the usual addition (+) and multiplication (×) operations. Which of the following are true? If false, indicate what property does not hold.

1. (C,+) is a group
2. (C,×) is a group
3. (C-{0},+) is a group
4. (C-{0},×) is a group
5. (C,+,×) is a ring
6. (C,+,×) is a commutative ring with identity
7. (C,+,×) is a field