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)

 
 be the three complex numbers then
  1. Z_1.(Z_2.Z_3)=(Z_1.Z_2).Z_3         
                                      Associative law of multiplication
  2.      1.Z=Z.1=ZMultiplicative identity..
  3. Z_1.Z_2=Z_2.Z_1Commutative law of multiplication
  4. 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

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