solutions to cambridge chapter 1E development (2 Viewers)

[vourzei]

anyone have worked solutions to cambridge chapter 1E development section i feel lost

 

[coolcat6778]

i would give but this would affect the scaling, so i will give after im all done

 

[coolcat6778]

cambridge sucks

author is such a patronizing pos

 

[killer queen]

anyone have worked solutions to cambridge chapter 1E development section i feel lost

what do you need help with?

 

[vourzei]

14, 16, 17, i just dk how to start

 

[spiderlemonade]

cambridge sucks

author is such a patronizing pos

what alternative textbooks would you recommend then
i only have cambridge and terry lee but the latter is too hard for me

 

[killer queen]

what do you need help with?

oof yeah this stuff, this admittedly doesn't take up too many marks usually in the HSC - I don't have the answers but I'll explain how I did it!

14. with these questions, I like to first write out the information it gives me - in this case, that the modulus = 1. then I'm like, okay, what am I trying to prove? what I did was express theta in terms of x and y (for z = x + iy), tan both sides, and used the double angle formula to prove that the RHS = the LHS after the tan. (you can do this because they give you the angle bounds already)...there's probably some geometric proof but I like doing things algebraically!

16. first, note down the vector representations of each side, so you know what you're trying to find. you should be able to instinctively see that the moduli of (z2-z1) and (z3-z1) are equal! then, you just should be able to write a line saying that there's a pi/3 angle between the two sides since multiplying by cis(pi/3) rotates the side by that. two equal sides subtending the an angle of pi/3 = equilateral triangle!

17. arg both sides! then simplify the arg expressions, and you should get the argument of p3 - p2 = argument of p2 - p1, which means p2 divides the angle between p3 and p1 exactly in 2, therefore it bisects!!

hope this helps!

what alternative textbooks would you recommend then
i only have cambridge and terry lee but the latter is too hard for me

terry lee is definitely unnecessary, cambridge is okay to start but honestly isn't the best, some of the questions later in exercises get a bit convoluted and just annoying
I've been using howardmathematics' free online one to bolster my learning, it's simple but gave me a good kickstart