Answer:
The product of given expression is (1+3i).
Step-by-step explanation:
The given expression is
[tex](1+i)(2+i)[/tex]
Using distributive property of multiplication, we get
[tex]1(2+i)+i(2+i)[/tex]
Using distributive property of multiplication again.
[tex]2+i+i(2)+i(i)[/tex]
[tex]2+i+2i+i^2[/tex]
[tex]2+i+2i-1[/tex] [tex][\because i^2=-1][/tex]
Combine like terms.
[tex](2-1)+(i+2i)[/tex]
[tex]1+3i[/tex]
Therefore the product of given expression is (1+3i).
