Chapter 7.2, Problem 14E

(a)

To determine

To prove: Addition in $ℂ$ defined by $\left(a,b\right)+\left(c,d\right)=\left(a+c,b+d\right)$ for $\left(a,b\right),\left(c,d\right)\in ℂ$ is associative.

(b)

To determine

To prove: Addition in $ℂ$ defined by $\left(a,b\right)+\left(c,d\right)=\left(a+c,b+d\right)$ for $\left(a,b\right),\left(c,d\right)\in ℂ$ is commutative.

(c)

To determine

To prove: $\left(0,0\right)$ is the additive identity in $ℂ$.

(d)

To determine

To prove: Additive inverse of $\left(a,b\right)\in ℂ$ is $\left(-a,-b\right)\in ℂ$.