Question

question 7 of 10
which choice is equivalent to the expression below?
\\(\sqrt{-121}\\)

a. \\(-\sqrt{11i}\\)

b. \\(11i\\)

c. \\(\sqrt{11i}\\)

d. \\(-\sqrt{11}\\)

e. \\(-11\\)

Explanation:

Step1: Recall the imaginary unit definition

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \), so we can rewrite \( \sqrt{-121} \) by factoring out \( -1 \) inside the square root.
\( \sqrt{-121} = \sqrt{121\times(-1)} \)

Step2: Use the property of square roots

Using the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0, b\geq0 \), and extended to complex numbers here), we have:
\( \sqrt{121\times(-1)}=\sqrt{121}\times\sqrt{-1} \)

Step3: Simplify the square roots

We know that \( \sqrt{121} = 11 \) and \( \sqrt{-1}=i \), so substituting these values in:
\( \sqrt{121}\times\sqrt{-1}=11\times i = 11i \)

Answer:

B. \( 11i \)