which expression is equivalent to (4 + 6i)^2?\n-20 + 48i\n8 + 12i\n16 - 36i\n20 + 48i

Explanation:

Step1: Apply the formula $(a + b)^2=a^{2}+2ab + b^{2}$

Here $a = 4$ and $b = 6i$, so $(4 + 6i)^2=4^{2}+2\times4\times6i+(6i)^{2}$

Step2: Calculate each term

$4^{2}=16$, $2\times4\times6i = 48i$, and $(6i)^{2}=6^{2}\times i^{2}=36\times(- 1)=-36$ (since $i^{2}=-1$)

Step3: Combine the terms

$16 + 48i-36=-20 + 48i$

Answer:

$-20 + 48i$