Question

question 14 (multiple choice worth 5 points) (01.06r lc) simplify \\(\sqrt{-49}\\). -7 7 -7i 7i

Explanation:

Step1: Recall imaginary unit definition

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \). So, we can rewrite \( \sqrt{-49} \) using this definition.

Step2: Simplify the square root

We know that \( \sqrt{-49} = \sqrt{49 \times (-1)} \). By the property of square roots \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0, b\geq0 \), but we extend it for complex numbers here), we have \( \sqrt{49\times(-1)}=\sqrt{49}\times\sqrt{-1} \). Since \( \sqrt{49} = 7 \) and \( \sqrt{-1}=i \), then \( \sqrt{-49}=7i \).

Answer:

7i (assuming the last option is "7i", so the answer is the option with "7i")