Verify the addition properties of the complex numbers.
Let z1=u+vι , z2=w+xι ,and z3=y+zι
thus z1+z2 is a complex no,then the closure law of (+) holds in the set of complex number C.
(ii) (z1+z2)+z3=[(u+vι)+(w+xι )]+(y+zι)
= (u+vι)+(w+xι )+(y+zι)
= (u+vι)+[(w+xι )+(y+zι)]
thus it shows that associative law of addition holds in the set of complex numbers C.
(iii)The additive identity in C is (0,0) such that
so it is hold in the set of complex numbers C.
(iv)Every complex number(x,y) has the additive inverse (-x,-y) i.e.,