Question

I have attached the questions I am having issues with

Answer 1

The questions address reflective thinking and research skills related to career success and academic writing, applicable in a college setting.

Step-by-step explanation:

The questions provided appear to be related to a range of topics and skills, including critical thinking and academic research, specifically within the scope of career success and academic writing. These questions encourage students to reflect on past experiences with writing papers in high school or college, delve into a specific problem they are interested in, and understand the process of writing a paper using the close reading approach. The goals seem to be identifying a problem of interest, its effects, and potential solutions, which is critical for developing strong analytical and problem-solving skills. Furthermore, the questions suggest a focus on sharing and discussing inquiries in a broader academic community, which aligns with the practices of higher education institutions.

Answer 2

let's keep in mind that i² = -1, so then

`\cfrac{-4-3i}{5i}\implies \cfrac{-4}{5i}-\cfrac{3i}{5i}\implies \cfrac{-4}{5i}-\cfrac{3}{5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{rationalizing the denominator}~\hfill }{\cfrac{-4}{5i}\cdot \cfrac{i}{i}\implies \cfrac{-4i}{5i^2}\implies \cfrac{-4i}{5(-1)}\implies \cfrac{-4i}{-5}\implies \cfrac{4}{5}i} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{-4}{5i}-\cfrac{3}{5}\implies \cfrac{4}{5}i-\cfrac{3}{5}\implies \stackrel{\textit{\LARGE a}}{-\cfrac{3}{5}}~~ + ~~\stackrel{\textit{\LARGE b}}{\cfrac{4}{5}i}`

now, let's recall that the conjugate of a binomial is simply the same thing but with a different sign in between, namely the conjugate of 2 - i is just 2 + i, so hmmm let's use that to rationalizing the denominator.

`\cfrac{-6-3i}{2-i}\implies \cfrac{-6-3i}{2-i}\cdot \cfrac{2+i}{2+i}\implies \cfrac{(-6-3i)(2+i)}{\underset{\textit{difference of squares}}{(2-i)(2+i)}} \\\\\\ \cfrac{(-6-3i)(2+i)}{2^2 - i^2}\implies \cfrac{-12-6i-6i-3i^2}{4-(-1)}\implies \cfrac{-12-12i-3(-1)}{4+1} \\\\\\ \cfrac{-12-12i+3}{5}\implies \cfrac{-9-12i}{5}\implies \stackrel{\textit{\LARGE a}}{-\cfrac{9}{5}}~~ \stackrel{\textit{\LARGE b}}{- ~~\cfrac{12}{5}i}`