Question

current learning objective: multiplying complex numbers
question 19
score: 0 of 1 point
evaluate the expression (-1 - 4i)(-3 - 5i)
a -17 + 17i
b -19 + 15i
c -21 + 13i
d -20 + 14i
submit answer attempts: 0/2
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Explanation:

Step1: Use FOIL method

\[

$$\begin{align*} (-1 - 4i)(-3 - 5i)&=(-1)\times(-3)+(-1)\times(-5i)+(-4i)\times(-3)+(-4i)\times(-5i)\\ &=3 + 5i+12i + 20i^{2} \end{align*}$$

\]

Step2: Recall \(i^{2}=-1\)

Since \(i^{2}=-1\), we substitute it into the above - expression:
\[

$$\begin{align*} 3 + 5i+12i + 20i^{2}&=3 + 5i+12i+20\times(-1)\\ &=3 + 5i+12i-20 \end{align*}$$

\]

Step3: Combine like - terms

\[

$$\begin{align*} 3 + 5i+12i-20&=(3 - 20)+(5i+12i)\\ &=-17 + 17i \end{align*}$$

\]

Answer:

A. \(-17 + 17i\)