Question

question 3 of 5
type the correct answer in the box.
consider this expression,
$(6 - 4i)(6 - 4i) - 3(7 - 11i)$
what is this expression written in the form $a + bi$, where $a$ and $b$ are rational numbers?

Explanation:

Step1: Expand the product \((6 - 4i)(6 - 4i)\)

Using the formula \((a - b)^2 = a^2 - 2ab + b^2\), where \(a = 6\) and \(b = 4i\), we have:
\[

$$\begin{align*} (6 - 4i)^2&=6^2 - 2\times6\times4i+(4i)^2\\ &= 36 - 48i + 16i^2 \end{align*}$$

\]
Since \(i^2=- 1\), then \(16i^2=-16\). So \((6 - 4i)^2=36 - 48i-16 = 20 - 48i\)

Step2: Expand \(-3(7 - 11i)\)

Using the distributive property \(a(b - c)=ab - ac\), we get:
\(-3\times7-(-3)\times11i=-21 + 33i\)

Step3: Combine the two results

Add the results from Step 1 and Step 2:
\((20 - 48i)+(-21 + 33i)=(20-21)+(-48i + 33i)=-1-15i\)

Answer:

\(-1 - 15i\)