Given:
[tex]\begin{gathered} x=1-3i \\ y=-1+6i \end{gathered}[/tex]the sum is:
[tex]\begin{gathered} x=1-3i \\ y=-1+6i \\ x+y=(1-3i)+(-1+6i) \\ x+y=1-3i-1+6i \\ =(1-1)+i(6-3) \\ =0+3i \end{gathered}[/tex]The product is:
[tex]\begin{gathered} x=1-3i \\ y=-1+6i \\ xy=(1-3i)(-1+6i) \\ xy=(1\times-1)+(1\times6i)+(-3i\times-1)+(-3i\times6i) \\ xy=-1+6i+3i-15i^2 \end{gathered}[/tex][tex]i^2=-1\text{ }[/tex][tex]\begin{gathered} xy=-1+6i+3i-15i^2 \\ xy=-1+8i-15(-1) \\ xy=-1+8i+15 \\ xy=14+8i \end{gathered}[/tex]
