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I am trusting you on the trig identities used to get z³ in part 1.3, because the list is too long and ctrl-f doesn't work for images. The power series expansion in 1.4 a) looks familiar, but also requires a bit of faith since I could not hope to derive it myself. The only step that left me really perplexed is 1.5 2). Are you just rearranging the equations and substituting? I didn't follow. From there it is clear how you get to cos(i) = 1.543..., and I suppose I should not be surprised that this falls outside the usual range of [-1, 1] for cosine. I was pleased with how much sense I was about to make from your notes, thanks for putting it together.