Multiplication of two complex numbers
let \[z_1\]=\[a+ib\] and and \[z_2=c+id\] be two complex number then multiplication of two complex numbers is given by
\[z_2z_1=a(c+id)+ib(c+id)=ac-bd+i(ad+bc)\]
where i is a complex number with value \[ \sqrt{-1}\]
Example 1
Let let \[z_1\]=\[2+i3\] and \[z_2=3+i5\]
then \[z_2z_1=a(c+id)+ib(c+id)=ac-bd+i(ad+bc)\]=6-15+i(9+10)=-10+19i
Example 2
Let let \[z_1\]=\[1+i2\] and \[z_2=1-2i\]
then then \[z_2z_1=1+4=5
Note (a+ib)(a-ib)=\[a^2+b^2\]
For ex- (5+i)(5-i)=26
(9-2i)(9+2i)=81+4=85
