Question

multiply. (-4 - 7i)(3 - 5i) enter your answer, in standard form, in the box.

Explanation:

Step1: Use FOIL method

\[

$$\begin{align*} (-4 - 7i)(3 - 5i)&=-4\times3+(-4)\times(- 5i)+(-7i)\times3+(-7i)\times(-5i)\\ \end{align*}$$

\]

Step2: Calculate each product

\[

$$\begin{align*} -4\times3&=-12\\ (-4)\times(-5i)& = 20i\\ (-7i)\times3&=-21i\\ (-7i)\times(-5i)&=35i^{2} \end{align*}$$

\]
Since \(i^{2}=-1\), then \(35i^{2} = 35\times(-1)=-35\)

Step3: Combine like - terms

\[

$$\begin{align*} &-12 + 20i-21i-35\\ =&(-12-35)+(20i - 21i)\\ =&-47 - i \end{align*}$$

\]

Answer:

\(-47 - i\)