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For part a), write z^6 - 1 = 0 as \left[z^2\right]^3 - 1^3 = 0 a difference of 2 cubes. Recall that a^3 - b^3 = (a - b)(a^2 + ab + b^2), therefore \left[z^2\right]^3 - 1^3 = (z^2 - 1)(z^4 + z^2 + 1) The roots where z \in Q are z = \pm1 . b) Consider z^6 - 1 = 0 as z^6 = 1 In...

Thanks.... I was sort of on the right track, but your solution has clarified my confusion. Cheers.

Hi all, This question comes from Cambridge Chapter 3(C) Q15. a) Show that every root of the equation is imaginary for (1+z)^{2n} + (1-z)^{2n} =0 b) Let the roots be represented by the points P_1, P_2, P_3, ... ,P_{2n} in the Argand diagram, and let O be the origin. Show that: OP^2_1 +...

Apologies for my ignorance, but what is "kurt"?

Can you please indicate what text book this came from. BTW I have the solution in PDF form if you wish.

Cheers. Thanks

So the 'high end mathematics' at year 12 in NSW is 1. Extension 1 2. Extension 2 Is that correct?

So If a student in NSW undergoing year 12 wanted to complete a full mathematics course, they would do 1. Advanced 2. Extension 1 3. Extension 2 That is, 3 mathematics subjects. Is this correct?

Hi all, I'm from Victoria, so I am unfamiliar with Mathematics course at year 12 level in NSW. If a student wishes to do a full complement of mathematics at year 12, what mathematics courses do they choose? Thanks in advance