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Let a, b be complex numbers that satisfy \frac{a}{b}+\frac{b}{a}+1=0. i) Prove that \frac{a^{3n}}{b^{3n}}+\frac{b^{3n}}{a^{3n}}=2 for n≥1, by using Mathematical Induction. - I proved true for n=1 and assumed true for n=k, just need help with Proving true for n=k+1 ii) Show that...

from here, \left(\frac{2cis\theta}{2cis-\theta}\right)^{n}=cis\ 2n\theta\ as\ required (kinda confuddled by 17. tho will come back to it later :D)

mx1 forum recently fr (thanks everyone <3)

Just realised - latex and other text shortcuts are on the BoS help page! Find it here: https://boredofstudies.org/help/bb-codes/

1992 3U HSC Q6c)ii) Show that 1-\frac{1}{2}\binom{n}{1}+\frac{1}{3}\binom{n}{2}-...+\left(-1\right)^{n}\frac{1}{n+1}\binom{n}{n}=\frac{1}{n+1} from 1+\binom{n}{1}x+\binom{n}{2}x^{2}+...+\binom{n}{n}x^{n}=\left(1+x\right)^{n}, I integrated both sides to get...

wha- 😰 {but srsly i like the calc for complex but are the vector stuff actually useful or gimmicky in exam conditions}

Thanks guys!! :)

I was just wondering how I would paste the code in [e.g. \frac{1}{2}+\sin \left(\frac{\frac{\left(2n+1\right)}{2}\theta }{\:2sin\left(\frac{\theta }{2}\right)}\right) ] BoS with the latex formatting to make it come out as maths form? [I'm just very confused with usage of latex in general goog...

q6c 1990 3u HSC hints to start ii)? Much thanks

I understand that IE is about the amount of energy needed to remove electrons and that electronegativity is the desire for an atom to gain electrons, but why do we need two things to describe essentially the same thing? Is it still relevant to understand PT trends for yr12 chem or is it kinda...

just looking quickly - i can tell ur meant to sub in x=cosx+1 into first equation, which leads to the same solution of 1<cosx+1<=3, therefore 0<cosx<=2 0<x<=pi/2

so would you basically describe how decreasing the coefficient A 'flattens' out the curve and lifts the sp above the x axis; leaving one solution?

yeah actually this was just a trap for all viewing rn - please help me with maths instead of this thread 🥺

nah, just curious

Since you cant delete accounts (and there are almost 600k accs registered), How many dyo reckon are still somewhat active on a monthly basis?

thats almost my school's median atar bruh 😭

[sorry in advance for potato webcam quality] For q (ii), How would you explain that leading coefficient A being smaller lead to it having one solution?\ Also, I calculated and desmosd that there is indeed one sp being one of two solutions when A=(3sqrt3)/3, but if A<-(3sqrt3)/3, then there is...

yeah, maybe 'metafictively elucidates the transformative symbol of the plane' but really it's just them linking plane=metaphor of transformation, therefore doesn't have any true qualities of metafiction (which involves the author stating that their narrative is a text), but I'm sure English...

Class has gone over texts and read through all of them - but hasn't learnt context or much work on writing comparatives yet - Best way to prepare for next term's English during the holidays? I might as well get started with context and quote, anything else I might need to do?

thank you