1. Verify the following algebraic properties of C.

i. The complex numbers 0 and 1 are the additive and multiplicative identities of C, respectively.

ii. Each z ∈ C has an additive inverse.

iii. Addition and multiplication of complex numbers is associative. In other words,

z + ( w + v )= ( z + w )+ v and z ( wv )= ( zw ) v for all z, w, v ∈ C.

2. Addition and multiplication of complex numbers is commutative. That is, z + w =

w + z and zw = wz for all z, w ∈ C.

3. Multiplication of complex numbers distributes over addition. That is, a ( z + w ) =

az + aw for all a, z, w ∈ C.

4. If z ∈ C is nonzero, then its multiplicative inverse is as given in (1.2.2).