Multiply or divide as indicated.
-$\sqrt{-2} \cdot \sqrt{-2}$
A) $2 \mathrm{i}$
B) -2
C) 2
D) $-2 \mathrm{i}$

Question

Quizplus · Accepted Answer

When you multiply $\sqrt{-2}$ by itself, you're essentially multiplying $-2$ by $-2$ under the square root, which simplifies to the square root of $4$, and the square root of $4$ is $2$. However, since the initial numbers were under a square root with a negative sign, the correct interpretation should be that the multiplication of two imaginary numbers (i.e., $\sqrt{-2} \cdot \sqrt{-2}$) results in a real number. The correct operation should consider the properties of imaginary numbers, where $i^2 = -1$, thus $(\sqrt{-2})^2 = -2$, not $2$ as previously explained. This correction addresses the mistake in the initial explanation regarding the handling of the square root of negative numbers and the properties of imaginary numbers.

Multiply or Divide as Indicated −2⋅−2\sqrt{-2} \cdot \sqrt{-2}−2​⋅−2​ A) 2i2 \mathrm{i}2i B) -2 C) 2 D)

Multiply or Divide as Indicated $\sqrt{-2} \cdot \sqrt{-2}$ A) $2 \mathrm{i}$ B) -2
C) 2
D)