Question 4 Simplify the following Expression \( \sqrt{-169}= \) If the answer is radical use sqrt( 5 ) to denote \( \sqrt{5} \) (use the correct radicand in the problem!) If the answer is complex use \( i \) to denote \( i \).

The expression \( \sqrt{-169} \) can be simplified by factoring out the negative sign. Since the square root of a negative number involves the imaginary unit \( i \), we have: \[ \sqrt{-169} = \sqrt{169} \cdot \sqrt{-1} = 13i \] Thus, the simplified expression is \( 13i \). In mathematics, imaginary numbers like \( i \) (which represents \( \sqrt{-1} \)) allow us to solve equations that have no real solutions, expanding our number system. This concept was critical in the development of complex analysis and applications in engineering, physics, and more, allowing us to model phenomena that real numbers alone cannot describe. If you want to delve deeper into imaginary and complex numbers, consider exploring "Complex Analysis" or "Imaginary Numbers in Engineering." There are various resources and textbooks that explain these concepts with examples, illustrations, and the fascinating ways they apply to real-world problems, particularly in signal processing and fluid dynamics.