\begin{tabular}{l} Write the squared complex number in the form $$ (a+b i) $$ \ $$ \qquad(4-3 i)^{2} $$ \ \hline\end{tabular}

Question

UpStudy AI · Accepted Answer

1. Write the square using the formula for binomials:  
   $$
   (4 - 3i)^2 = (4)^2 + 2 \cdot 4 \cdot (-3i) + (-3i)^2
   $$

2. Compute each term:  
   - $$ (4)^2 = 16 $$  
   - $$ 2 \cdot 4 \cdot (-3i) = -24i $$  
   - $$ (-3i)^2 = 9i^2 $$

3. Replace $$ i^2 $$ with $$-1$$:  
   $$
   9i^2 = 9(-1) = -9
   $$

4. Combine the real and imaginary parts:  
   $$
   16 - 9 - 24i = 7 - 24i
   $$

Thus, the squared complex number in the form $$ a + bi $$ is  
$$
7 - 24i
$$
$$(4 - 3i)^2 = 7 - 24i$$

\begin{tabular}{l} Write the squared complex number in the form \( (a+b i) \) \\ \( \qquad(4-3 i)^{2} \) \\ \hline\end{tabular}