Question

question 12
1 pts
-10i
options:
√-10
√-100
-√-10
-√-100

Explanation:

Step1: Recall the imaginary unit definition

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \), so \( \sqrt{-a}=i\sqrt{a} \) for \( a>0 \).

Step2: Analyze each option

• Option 1: \( \sqrt{-10}=i\sqrt{10}\approx 3.16i \), not \(-10i\).
• Option 2: \( \sqrt{-100}=i\sqrt{100} = 10i \), not \(-10i\).
• Option 3: \( -\sqrt{-10}=-i\sqrt{10}\approx - 3.16i \), not \(-10i\).
• Option 4: \( -\sqrt{-100}=-i\sqrt{100}=- 10i \), which matches the given \(-10i\).

Answer:

D. \(-\sqrt{-100}\) (assuming the options are labeled A to D as A. \(\sqrt{-10}\), B. \(\sqrt{-100}\), C. \(-\sqrt{-10}\), D. \(-\sqrt{-100}\))