Questions: Which of the following shows sqrt(-16) simplified and written as a complex number? 4+i -4 i 16 i 0+4 i

Solution Steps

To simplify \(\sqrt{-16}\) and express it as a complex number, we need to recognize that the square root of a negative number involves the imaginary unit \(i\), where \(i = \sqrt{-1}\). Therefore, \(\sqrt{-16}\) can be rewritten as \(\sqrt{16} \times \sqrt{-1}\). The square root of 16 is 4, and \(\sqrt{-1}\) is \(i\). Thus, \(\sqrt{-16}\) simplifies to \(4i\).

We need to simplify the expression \(\sqrt{-16}\). This involves recognizing that we are dealing with a negative number under the square root.

Using the property of square roots, we can separate the expression as follows: \[ \sqrt{-16} = \sqrt{16} \times \sqrt{-1} \]

We know that: \[ \sqrt{16} = 4 \quad \text{and} \quad \sqrt{-1} = i \] Thus, we can combine these results: \[ \sqrt{-16} = 4 \times i = 4i \]

Final Answer