Question

Can someone help me understand how to solve Multiplying complex number. Warm up question ungraded.

Answer 1

The given complex expression is

`(-2-4i)(5+6i)`

The expression can be expanded as follows

`(-2-4i)(5+6i)=-2(5+6i)-4i(5+6i)`

Multiply the numbers

`\begin{gathered} -2(5+6i)-4i(5+6i) \\ =-10-12i-20i-24i^2 \end{gathered}`

Simplify further

`\begin{gathered} -10-12i-20i-24i^2 \\ =-10-32i-24i^2 \end{gathered}`

But

`i^2=-1`

Hence, it follows

`\begin{gathered} -10-32i-24i^2 \\ =-10-32i-24(-1)^{} \\ =-10-32i+24 \\ =14-32i \end{gathered}`

Therefore, the answer is

`14-32i`