1. **State the problem:** Express $-3\sqrt{-100}$ as a complex number. 2. **Recall the rule for square roots of negative numbers:** For any positive number $a$, $\sqrt{-a} = \sqrt{a}i$, where $i$ is the imaginary unit with the property $i^2 = -1$. 3. **Apply the rule:** $$\sqrt{-100} = \sqrt{100}i = 10i$$ 4. **Multiply by -3:** $$-3 \times 10i = -30i$$ 5. **Final answer:** $$-3\sqrt{-100} = -30i$$ This is the complex number form of the expression.