Question

simplify.
$(-4 + 3i)^2$
write your answer in the form $a + bi$.

Explanation:

Step1: Expand using square formula

Recall $(a+b)^2 = a^2 + 2ab + b^2$. Let $a=-4$, $b=3i$.
$$(-4 + 3i)^2 = (-4)^2 + 2(-4)(3i) + (3i)^2$$

Step2: Calculate each term

Compute each part separately:
$(-4)^2 = 16$, $2(-4)(3i) = -24i$, $(3i)^2 = 9i^2$
$$= 16 - 24i + 9i^2$$

Step3: Substitute $i^2=-1$

Replace $i^2$ with $-1$ and simplify:
$$= 16 - 24i + 9(-1) = 16 - 9 - 24i$$

Step4: Combine constant terms

Subtract constants to get final form:
$$= 7 - 24i$$

Answer:

$7 - 24i$