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    help with proof question

    need help from part b onwards, including a for context.
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    Recursive Induction

    A sequence is defined by an+1 = 1/2 (an + 2/an) where a1=1 and n is a positive integer Use induction to show that (an - √2)/an + √2) = ((1 - √2)/(1+√2))^2^(n-1)
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    Polynomials with Trigonometric roots and a request

    Hey, I've been stuck on this question for a while so was hoping if someone could help me with parts c and d. (parts a and b given for context) a) obtain cos6θ as a polynomial in cosθ. b) Hence show that x=cos ((2k+1) π)/12 where k=0,1,2,3,4,5 are the roots of the equation 32x^6-48x^4+18x^2-1=0...
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    Geometrical Interpretation of Complex Numbers

    Can someone send working out for/explain this question: The points A and B represent the complex numbers z1 and z2 respectively, where modulus of z1=1 and arg(z1)=theta OB is root3 times as long as OA and <AOB = 90. B represents the complex number z2 Which complex number re[resents z2-z1?
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    Help with a proof

    Hi, I was struggling with this question in the Cambridge textbook so I stumbled upon a solution online which seems to work, however I dont understand how the person thought of this and why this works. I also dont understand what the part about the pi -pi stuff is about either If someone who...
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    Complex Help

    Can you guys help me with how to do this question? 17. the points P1, P2 and P3 represent the complex numbers z1, z2 and z3 respectively. If z2/z1 = z3/z2 , show that OP2 bisects angle P1OP3.
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