Question

calcule; ( A (3 + 5 i) . (4-2 i ) (B (5+I). ( 2 + I)

Answer 1

Vamos aplicar a propriedade distributiva da multiplicação.

a)

$(3+5i)~.~(4-2i)~=\\\\\\=~3~.~4~+~3~.~(-2i)~+~5i~.~4~+~5i~.~(-2i)\\\\\\=~12~-~6i~+~20i~-~10i^2\\\\\\=~12~+~14i~-~10\,.\,(-1)\\\\\\=~12~+~14i~+~10\\\\\\=~\boxed{22~+~14i}$

b)

$(5+i)~.~(2+i)~=\\\\\\=~5~.~2~+~5~.~i~+~i~.~2~+~i~.~i\\\\\\=~10~+~5i~+~2i~+~i^2\\\\\\=~10~+~7i~-~1\\\\\\=~\boxed{9~+~7i}$