Re: Hard complex number question
I understand what you mean by
"just one Q, with this question, did you know to expand the binomials (evetnually leading to a quadratic in x^2) or just tried it in an attempt to answer the Q?"
I think what he did was looked at the question, noting that the answer was in terms of tan^2 [on the RHS] and there was a square root [on the LHS], recognising the quadratic formula form.
As you said, it is easy to see that the expression w.r.t z cancels to form a quartic [z^4] and I would have concluded that the quadratic solution [from the quadratic formula] to the quartic must be in terms of tan^2, meaning that the polynomial must be expanded.
You have to be able to intuitively see the link between the "tan^2=" result of the question and the "z^4" result of the expansion of the previous part. I had to read it a couple of times. lol.
hope this makes sense.