(i) Addition is associative $(z+w)+t=z+(w+t);$

(ii) multiplication is associative $(zw)t=z(wt)$;

(iii) addition is commutative $z+w=w+z$;

(iv) multiplication is commutative $zw=wz$;

(v) multiplication is distributive over addition $t(w+z)=tw+tz$;

(vi) $0=0+i0$ satisfies $0+z=z$;

(vii) $(x+iy)+(-x-iy)=0$;

(viii) $1=1+i0$ satisfies $1z=z$;

(ix) $\overline{zw}=\bar{z}\bar{w}$;

(x) $\overline{z+w}=\bar{z}+\bar{w}$;

(xi) the conjugate of $\bar{z}$ is $z$ itself;

(xii) $|z|^{2}=z\bar{z}>0$ for all $z\neq 0$.