Question

Part1: Explain, in complete sentences, how adding and subtracting radicals and complex numbers is similar to adding and subtracting polynomials.

Part 2: Give one example of an addition or subtraction problem of radicals.

Part 3: Give one example of an addition or subtraction problem of complex numbers.

Answer 1

So, what can you see that is similar between these:
\((x^2 + 2x + 3) + (3x^2 + 2) = (3 + 1)x^2 + 2x + (3 + 2) = \color{green}{4x^2 + 2x + 5}\)
\((2 + 2i) + (4 - 3i) = (2 + 4) + (2 + -3)i = \color{green}{6 - i}\)
\((\sqrt{3}) + (2\sqrt{3}) = (2 + 1)\sqrt{3} = \color{green}{3\sqrt{3}}\)

Don't we have to consider which \(parts\) we add together in these? That might be a good hint for writing the explanation.