1. Let's start by understanding the problem: why does $2i^2$ become $-4$? 2. Recall the definition of the imaginary unit $i$: by definition, $i^2 = -1$. 3. Now, substitute $i^2$ with $-1$ in the expression $2i^2$: $$2i^2 = 2 \times (-1)$$ 4. Multiply the numbers: $$2 \times (-1) = -2$$ 5. So, $2i^2$ equals $-2$, not $-4$. If you saw $2i^2$ become $-4$, it might be a mistake or a different expression was involved. 6. For example, if the expression was $2 \times (2i^2)$, then: $$2 \times (2i^2) = 2 \times 2 \times (-1) = -4$$ 7. But strictly for $2i^2$, the value is $-2$. Final answer: $2i^2 = -2$.