Question

question 35 of 41
which of the following is equivalent to the expression below?
\\(\sqrt{-16}\\)

a. \\(4i\\)
b. \\(-4\\)
c. \\(4\\)
d. \\(-4i\\)

Explanation:

Step1: Recall the definition of imaginary unit

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \). So we can rewrite \( \sqrt{-16} \) as \( \sqrt{16\times(-1)} \).

Step2: Use the property of square roots

Using the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0, b\geq0 \), and here we extend it for complex numbers), we have \( \sqrt{16\times(-1)}=\sqrt{16}\times\sqrt{-1} \).

Step3: Simplify the square roots

We know that \( \sqrt{16} = 4 \) and \( \sqrt{-1}=i \), so substituting these values in, we get \( 4\times i = 4i \).

Answer:

A. \( 4i \)