Question

Simplify (4+2i)(1+5i)

Answer 1

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:

`\mleft(4+2i\mright)\mleft(1+5i\mright)=4\cdot1+4\cdot5i+2i\cdot1+2i\cdot5i`

Now we can solve:

`4+20i+2i+(2\cdot5)i^2`

i^2 is (-1). Then:

`\begin{gathered} 4+22i+10(-1) \\ 4-10+22i \\ -6+22i \end{gathered}`

-6+22i is the simplified expression