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Multiply (1+3i)(5+i)\left(1 + 3 i\right) \left(5 + i\right)(1+3i)(5+i) using FOIL.
((1)+(3i))((5)+(i))=(1)(5)⏟First+(1)(i)⏟Outer+(3i)(5)⏟Inner+(3i)(i)⏟Last=5+i+15i−3=2+16i\left({\color{red}\left(1\right)} + {\color{purple}\left(3 i\right)}\right) \left({\color{green}\left(5\right)} + {\color{blue}\left(i\right)}\right) = \underbrace{{\color{red}\left(1\right)} {\color{green}\left(5\right)}}_{\text{First}} + \underbrace{{\color{red}\left(1\right)} {\color{blue}\left(i\right)}}_{\text{Outer}} + \underbrace{{\color{purple}\left(3 i\right)} {\color{green}\left(5\right)}}_{\text{Inner}} + \underbrace{{\color{purple}\left(3 i\right)} {\color{blue}\left(i\right)}}_{\text{Last}} = 5 + i + 15 i - 3 = 2 + 16 i((1)+(3i))((5)+(i))=First(1)(5)+Outer(1)(i)+Inner(3i)(5)+Last(3i)(i)=5+i+15i−3=2+16i
(1+3i)(5+i)=2+16i\left(1 + 3 i\right) \left(5 + i\right) = 2 + 16 i(1+3i)(5+i)=2+16iA