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To simplify the expression \(-2i \cdot (-3i)\), let's proceed with the following steps:

1. **Multiply the constants**: \(-2 \times -3 = 6\).
2. **Multiply the imaginary units**: \(i \times i = i^2\).

Since \(i^2 = -1\), we get:
\[
6 \cdot i^2 = 6 \cdot (-1) = -6
\]

Therefore, the simplified answer is \(-6\).

Would you like more details or have any questions?

Here are some related questions to explore further:

1. What happens when we multiply two imaginary numbers with different signs?
2. How is \(i^2 = -1\) derived, and what does it represent in complex numbers?
3. What would the result be if both imaginary numbers had positive signs?
4. How would the answer change if we had a real number multiplied by an imaginary number?
5. What is the effect of squaring an imaginary number?

**Tip:** Remember, \(i^2 = -1\) is a fundamental property of imaginary numbers, and it helps simplify expressions involving powers of \(i\).

Learn how to simplify the expression -2i(-3i) by understanding the multiplication of imaginary numbers and the fundamental property i^2 = -1. This problem demonstrates key concepts in complex numbers and is suitable for Grade 10 students.

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