Question

algebra 2a semester online practice
complete this assessment to review what you’ve learned. it will not cou
evaluate the subtraction ((-sqrt{16} + 8i) - (32 - sqrt{-16})) (1 point)

(-28 + 12i)

(-36 + 4i)

(-36 + 12i)

(-40 + 16i)

Explanation:

Step1: Simplify square roots

Simplify $\sqrt{16}$ and $\sqrt{-16}$. We know that $\sqrt{16} = 4$ and $\sqrt{-16}=\sqrt{16}\cdot\sqrt{-1}=4i$ (since $i = \sqrt{-1}$). So the expression becomes $(- 4 + 8i)-(32 - 4i)$.

Step2: Distribute the subtraction

Distribute the negative sign to the terms inside the second parentheses: $-4 + 8i-32 + 4i$.

Step3: Combine like terms

Combine the real parts and the imaginary parts separately. For real parts: $-4-32=-36$. For imaginary parts: $8i + 4i = 12i$. So the result is $-36 + 12i$.

Answer:

-36 + 12i (corresponding to the option: $-36 + 12i$)