Closure law: multiplication of two complex numbers is a complex number, i.e. the product z1z2 is a complex number for all complex numbers z1 and z2.
Commutative law: for any two complex numbers z1 and z2, z1・z2 = z2・z1
Associative law: for any three complex numbers z1, z2 and z3 , (z1・z2)・z3 = z1・(z2 ・z3)
Multiplicative identity: if the multiplication of a complex number z1 with another complex number z2 is z1, then z2 is called the multiplicative identity. We have z・1 = z = 1・z, so 1 is the multiplicative identity.
Multiplicative inverse: For every non-zero complex z = a + ib, (a ≠ 0,b ≠ 0 ) we have the complex number called the multiplicative inverse of z.
Distributive law : for any three complex numbers z1, z2 and z3 , z1・(z2 + z3) = z1・z2 + z1・z3 and (z1 + z2)・z3 = z1・z3 + z2・z3