Question

multiply.
$(6 - 6i)(-2 + 4i)$
write your answer as a complex number in standard form.

Explanation:

Step1: Apply the distributive property (FOIL method)

We multiply each term in the first complex number by each term in the second complex number:
\[

$$\begin{align*} (6 - 6i)(-2 + 4i)&=6\times(-2)+6\times4i-6i\times(-2)-6i\times4i\\ &=-12 + 24i + 12i - 24i^2 \end{align*}$$

\]

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

Recall that \(i^2 = - 1\), so we substitute \(-1\) for \(i^2\) in the expression:
\[

$$\begin{align*} -12 + 24i + 12i - 24i^2&=-12 + 24i + 12i - 24\times(-1)\\ &=-12 + 24i + 12i + 24 \end{align*}$$

\]

Step3: Combine like terms

Combine the real parts and the imaginary parts separately:
The real parts are \(-12\) and \(24\), and the imaginary parts are \(24i\) and \(12i\).
\[

$$\begin{align*} (-12 + 24)+(24i + 12i)&=12 + 36i \end{align*}$$

\]

Answer:

\(12 + 36i\)