multiply and simplify the following complex numbers: $(-1 + 4i) \cdot (4 - 3i)$

Question

Accepted Answer

# Explanation:
## Step1: Use the distributive property (FOIL method)
Multiply each term in the first complex number by each term in the second complex number:
$$
\begin{align*}
(-1 + 4i) \cdot (4 - 3i)&= -1 \cdot 4 + (-1) \cdot (-3i) + 4i \cdot 4 + 4i \cdot (-3i)\
&= -4 + 3i + 16i - 12i^2
\end{align*}
$$
## Step2: Simplify using $i^2 = -1$
Recall that $i^2 = -1$, so substitute $-1$ for $i^2$ in the expression:
$$
\begin{align*}
-4 + 3i + 16i - 12i^2&= -4 + 3i + 16i - 12(-1)\
&= -4 + 3i + 16i + 12
\end{align*}
$$
## Step3: Combine like terms
Combine the real parts and the imaginary parts separately:
$$
\begin{align*}
-4 + 12 + (3i + 16i)&= 8 + 19i
\end{align*}
$$
# Answer:
$8 + 19i$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the distributive property (FOIL method)

Step2: Simplify using \(i^2 = -1\)

Step3: Combine like terms

Answer: