a) Determine the roots of z^4 + 1 = 0 in cartesian form. Plot them on an Argand diagram.
b) Write z^4 + 1 in terms of real quadratic factors/
c) Divide by z^2 to show that cos(2x) = (cos(x) - cos(45)(cos(x) - cos(135))
Need help with part (c) thanks
Last edited by jathu123; 22 Oct 2018 at 6:13 PM.
2017
4u99 - 3u98 - EngAdv88 - Phys94 - Chem94
Atar : 99.55
Course: Engineering(Hons)/Commerce @ UNSW
ATAR is just a number
thank you, i didnt write part (c) wrong by the way i think you read it wrong because it says: [2](cos(x) + cos(45))(cos(x) + cos(135))
2017
4u99 - 3u98 - EngAdv88 - Phys94 - Chem94
Atar : 99.55
Course: Engineering(Hons)/Commerce @ UNSW
ATAR is just a number
Not sure this hangs together properly?
When you say z^4+1=(z^2-root2z+1)(z^2+root2z+1) this is a factorization of a polynomial. It is an identity true for every complex z.
Suddenly in the next line you are assuming that |z|=1?
For example if z=7 then most certainly 49+1/49 is not 2cos(anything)?
Proof as it stands is quite muddy and misleading.
Best to at least state somewhere that you are restricting the identity to the unit circle.
Last edited by peter ringout; 20 Nov 2018 at 11:39 PM.
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