Question

question 11
1 pts
8i
-√64
√-64
√-8
-√-8

Explanation:

Step1: Recall the definition of imaginary unit

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \), and for any non - negative real number \( a \), \( \sqrt{-a}=\sqrt{a}\times\sqrt{-1}=i\sqrt{a} \).

Step2: Analyze each option

• Option 1: \( -\sqrt{64}=- 8 \), which is a real number, not an imaginary number of the form \( 8i \).
• Option 2: \( \sqrt{-64}=\sqrt{64}\times\sqrt{-1} = 8i \) (since \( \sqrt{64} = 8 \) and \( \sqrt{-1}=i \)).
• Option 3: \( \sqrt{-8}=\sqrt{8}\times\sqrt{-1}=2\sqrt{2}i

eq8i \).

• Option 4: \( -\sqrt{-8}=-\sqrt{8}\times\sqrt{-1}=- 2\sqrt{2}i

eq8i \).

Answer:

\(\boldsymbol{\sqrt{-64}}\) (corresponding to the option \(\boldsymbol{\sqrt{-64}}\))