complex numbers (1 Viewer)

[shsshs]

hey im stuck in this past paper question. would realli lyk help

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i) Find the roots of z = 1 (i can do this part)

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explain why ( (z-1) / z) = 1 only has nine roots,
show the roots of this equation are

z = 1/2 (1 + i cot (kPI/10) ), k = 1,2,3...,9

 

[Riviet]

[(z-1)/z]¹⁰=1
(z-1)¹⁰=z¹⁰
If you expanded LHS, you'd get z¹⁰-z⁹...+1, which means you can subtract the z¹⁰ from both sides and you will have a polynomial with degree 9, giving 9 solutions. I don't know how to do the last bit though.

 

[who_loves_maths]

hey im stuck in this past paper question. would realli lyk help

...

z = 1/2 (1 + i cot (kPI/10) ), k = 1,2,3...,9

http://community.boredofstudies.org/14/mathematics-extension-2/115239/solve.html
has a similar question in which the solution to getting your desired result is exactly the same save for a few different algebraic manipulations along the way.