Question

question 1 of 5
select the correct answer.
what is the value of this expression?
(10 - 4i)(4 - 5i) + (-15 + 20i)
5 + 46i
55 + 54i
55 - 54i
5 - 46i

Explanation:

Step1: Multiply the complex numbers

First, we multiply \((10 - 4i)(4 - 5i)\) using the distributive property (FOIL method).
\[

$$\begin{align*} (10 - 4i)(4 - 5i)&=10\times4+10\times(-5i)-4i\times4-4i\times(-5i)\\ &=40 - 50i - 16i + 20i^{2} \end{align*}$$

\]
Since \(i^{2}=- 1\), we substitute that in:
\[

$$\begin{align*} 40 - 50i - 16i + 20\times(-1)&=40 - 50i - 16i - 20\\ &=(40 - 20)+(-50i-16i)\\ &=20-66i \end{align*}$$

\]

Step2: Add the remaining complex number

Now we add \((-15 + 20i)\) to the result from Step 1:
\[

$$\begin{align*} (20-66i)+(-15 + 20i)&=(20-15)+(-66i + 20i)\\ &=5-46i \end{align*}$$

\]

Answer:

\(5 - 46i\) (the option: 5 − 46i)