Question

perform the indicated operations.
$(-5 + \sqrt{-9})^2$
$(-5 + \sqrt{-9})^2 = \square$
(simplify your answer. type your answer in the form $a + bi$.)

Explanation:

Step1: Rewrite radical as imaginary number

$\sqrt{-9} = 3i$, so the expression becomes $(-5 + 3i)^2$

Step2: Expand using square formula

Use $(a+b)^2 = a^2 + 2ab + b^2$:
$$(-5)^2 + 2(-5)(3i) + (3i)^2$$

Step3: Calculate each term separately

$$\begin{align*} (-5)^2 &= 25 \\ 2(-5)(3i) &= -30i \\ (3i)^2 &= 9i^2 = 9(-1) = -9 \end{align*}$$

Step4: Combine real and imaginary terms

$25 - 9 - 30i = 16 - 30i$

Answer:

$16 - 30i$