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Yeah, I was on that track but didn't think it was right. May I see the solution?

$If the points z_1, z_2, z_3 lie\ on\ a\ circle\ through\ the\ origin,\ prove\ that\ the\ points\ \frac{1}{z_1},\frac{1}{z_2},\frac{1}{z_3}\ are\ collinear Can someone start me off, because I've got no clue what to do, but not finish it. I wanna have a go. Also need help with the last...

I'm stuck on another question $The points A, B and C form a triangle whose vertices present the complex numbers \alpha ,\beta and \gamma respectively. I've proved that if \frac{\gamma -\beta }{\gamma -\alpha }=Cis\frac{\pi }{3} then it's an equilateral triangle. But I need help to show...

Got another one that I can't do. Prove |1-zW|^2-|z-w|^2=(1-|z|^2)(1-|w|^2) for any pair of complex numbers z and w, where W is the conjugate of w

Man, are you a genius?

Ok. I tried taking modulus and I realised I couldn't get it. The question was. If a+ib=\frac{(x+i)^2}{2x-i} Prove a^2+b^2=\frac{(x^2+1)^2}{4x^2+1}

If a+ib=\frac{(x+1)^2}{2x-i} Prove a^2+b^2=\frac{(x^2+1)^2}{4x^2+1} I've been trying to do this for half an hour and I'm getting nowhere.

Yeah thanks, but how would you know you had to add. I tried doing it by subing into the equation, trying to prove LHS=RHS I got up to. LHS = (z_2)^2cis\frac{2\pi }{3}+(z_1)^2cis\frac{-2\pi }{3} But cant seem to get it to equal z1z2

If A,B represent z1 and z2 OAB is equilateral, prove (z_1)^2+(z_2)^2=z_1z_2 What am I doing wrong? Or do I have to do soething with multiplying by Cis pi/3 LHS= |(z_1)^2|+|(z_2)^2| |z_1|^2+|z_2|^2 Let common modulus be z |z|^2+|z|^2 2|z|^2 RHS= |z_1z_2| |z_1||z_2|...

No idea how to do this one... If\ z=x+iy\ and\ z^2=a+ib Prove 2x^2=\sqrt{(a^2+b^2)}+a

My god thanks. Cannot believe I missed that.

Yeah, I was using identities and I always seem to be stuck. Can you try for me because it's the way I'v learnt to do it.

it was meant to be -2<k<2

Yeah it's the full queston and you're right. I got the question from my tutor. I've got another one here. I've partially solved it. \frac{1}{1+z}=\frac{1}{2}(1-itan\frac{\Theta }{2}) I'm trying to prove that. I've got up to \frac{1}{2}(\frac{cos\frac{\Theta }{2}(cos\frac{\Theta...

I don't get the discriminate part. What relevance does it have?

Show that the equation x^2 +kx +1 = 0 has complex roots with unit modulus provided -2<k<2

Thanks for the info. In an unrelated question, How do you find the lim as x approaches infinity, or the asymptote, of x^2 - y^2 + xy = 5

Well here are some queries. If the slope of the graph of f'(x) is negative, what about the slope of f(x) What does the x-intercept of f'(x) indicate? What does the stationary point of f'(x) indicate? If the graph of f'(x) is above the x-axis, what does it indicate?

Yeah like that. What else do I have to know?

Can somebody teach me some general tips in reading the graph of the derivative.