3 Assignment \( 1 \leftarrow \quad \) Express in terms of \( i \). \( \sqrt{-36} \)

To express \(\sqrt{-36}\) in terms of \(i\), we start by recognizing that the square root of a negative number can be represented using the imaginary unit \(i\), where \(i = \sqrt{-1}\). Thus, we can rewrite \(\sqrt{-36}\) as follows: \[ \sqrt{-36} = \sqrt{36} \cdot \sqrt{-1} = 6i. \] So, the expression simplifies to \(6i\). Another fun fact about \(i\) is that it is not just a symbol; it represents a whole new realm of numbers called complex numbers! Complex numbers combine real and imaginary parts, expanding the boundaries of traditional mathematics. You could even say \(i\) is the superhero of the math world, helping us solve equations that would otherwise have no solutions in the realm of real numbers! When dealing with complex numbers, understanding operations with \(i\) is crucial. For example, a common mistake is assuming that \(i^2 = 2\) instead of knowing that \(i^2 = -1\). Remembering this is key in simplifying expressions—like realizing that \(i^4 = 1\) can help you tackle more complex equations with ease. Always keep practicing those power cycles of \(i\), and you’ll become a pro at navigating the imaginary plane in no time!