Reference no: EM13842271
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).
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