Question

Simplify the expression: (7 + 9i)(8 – 10i). 1) 56 + 2i + 902) 56 + 2i – 90i23) 97 + 72i4) 146 + 2i

Answer 1

The given expression is:

`(7+9i)(8-10i)`

Expand the binomial, noting that for a complex number, i²=-1:

`\begin{gathered} (7+9i)(8-10i)=7(8-10i)+9i(8-10i) \\ \Rightarrow(7+9i)(8-10i)=56-70i+72i-90i^2 \end{gathered}`

Substitute i²=-1 into the expression:

`\begin{gathered} (7+9i)(8-10i)=56-70i+72i-90i^2 \\ \Rightarrow(7+9i)(8-10i)=56-70i+72i-90(-1)=56-70i+72i+90 \\ \text{Collect like terms and simplify:} \\ \Rightarrow(7+9i)(8-10i)=56+90-70i+72i=146+2i \end{gathered}`

The correct answer is option 4.