Question

Find the sum and product of the complex numbers 1 - 3 i and - 1 + 6 i. The sum is __(Type in form a+bi)The product ia __(Type in form a+bi)

Answer 1

Given:

`\begin{gathered} x=1-3i \\ y=-1+6i \end{gathered}`

the sum is:

`\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}`

The product is:

`\begin{gathered} x=1-3i \\ y=-1+6i \\ xy=(1-3i)(-1+6i) \\ xy=(1*-1)+(1*6i)+(-3i*-1)+(-3i*6i) \\ xy=-1+6i+3i-15i^2 \end{gathered}`
`i^2=-1\text{ }`
`\begin{gathered} xy=-1+6i+3i-15i^2 \\ xy=-1+8i-15(-1) \\ xy=-1+8i+15 \\ xy=14+8i \end{gathered}`