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Complex Numbers Question HELPPPP !!! (1 Viewer)

_mysteryatar_

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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
 

jathu123

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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
pretty sure it should be 1/2 cos(2x) for (c)



meant to write x instead of theta rip

Incase you get confused in the 3rd line, I divided the terms of each factor on the RHS by z (which accounts to dividing the whole side by z^2)
 
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_mysteryatar_

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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))
 

jathu123

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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))
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
no worries!
lol idk if im blind or my laptop display is being dodgy
 

peter ringout

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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.
 
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