The simplyfied expression is: -6 + 22i
To multiply two complex numbers, we need to apply distributive propiertie with each term of each parentheses. In this case:
[tex]\mleft(4+2i\mright)\mleft(1+5i\mright)=4\cdot1+4\cdot5i+2i\cdot1+2i\cdot5i[/tex]Now we can solve:
[tex]4+20i+2i+(2\cdot5)i^2[/tex]i^2 is (-1). Then:
[tex]\begin{gathered} 4+22i+10(-1) \\ 4-10+22i \\ -6+22i \end{gathered}[/tex]-6+22i is the simplified expression
