Answer:
(a) [tex]w=2+5i-6=-4+5i[/tex]
Multiplicative inverse of w will be [tex]\frac{1}{-4+5i}[/tex]
(B) As w is same as the product of [tex]z_1\ and\ z_2[/tex]
So there multiplicative inverse will also be same
Step-by-step explanation:
We have given two complex numbers
[tex]z_1=1+i[/tex] and [tex]z_2=3+2i[/tex]
(a) First we have to find [tex]w=z_1z_2[/tex]
So [tex]w=(1+i)(2+3i)=2+3i+2i+6i^2=2+5i+6i^2[/tex]
As we know that [tex]i^2=-1[/tex]
So [tex]w=2+5i-6=-4+5i[/tex]
Multiplicative inverse :
It is that number when multiply with the number which we have have to find the multiplicative inverse gives result as 1
So multiplicative inverse of w will be [tex]\frac{1}{-4+5i}[/tex]
Because when we multiply [tex]-4+5i[/tex] with [tex]\frac{1}{-4+5i}[/tex] it gives result as 1
(b) As w is same as the product of [tex]z_1\ and\ z_2[/tex]
So there multiplicative inverse will also be same
