Properties of complex numbers w.r.t multiplication

Properties of complex Numbers

If $Z_1=(x_1,y_1),Z_2=(x_2,y_2),Z_3=(x_3,y_3)$

$Z_1.(Z_2.Z_3)=(Z_1.Z_2).Z_3$

Associative law of multiplication
$1.Z=Z.1=Z$ Multiplicative identity..
$Z_1.Z_2=Z_2.Z_1$ Commutative law of multiplication
For each non-zero $\fn_cm z=(x, y) \in R^2, x \neq 0 \,\or\,\ y \neq 0\\ then \,\,\ z^*=(\frac{x}{x^2+y^2},\frac{-y}{x^2+y^2})\\such\,\ that \\ z.z^*=(1,0)=1$