Complex No's Question (1 Viewer)

[shaon0]

Q5:
bi) Show that the roots of z^10=1 are given by:
z=cis(r*pi/5), r=1,2,3,...,9
DONE

ii) Explain why the equation ((z-1)/z)^10=1. Only has nine roots. Show that the roots of ((z-1)/z)^10=1 are given by z=(0.5)(1+icot(r*pi/5)), r=1,2,...,9

I can't show that the roots are given by z=(0.5)(1+icot(r*pi/5)), r=1,2,...,9.
Any help would be appreciated.

 

[Drongoski]

Why only 9 roots

 

[untouchablecuz]

Q5:
bi) Show that the roots of z^10=1 are given by:
z=cis(r*pi/5), r=1,2,3,...,9
DONE

ii) Explain why the equation ((z-1)/z)^10=1. Only has nine roots. Show that the roots of ((z-1)/z)^10=1 are given by z=(0.5)(1+icot(r*pi/5)), r=1,2,...,9

I can't show that the roots are given by z=(0.5)(1+icot(r*pi/5)), r=1,2,...,9.
Any help would be appreciated.

here you go

 

[untouchablecuz]

for k = 2m = 2, 4, 6, 8, ..., 18

therefore

z = (0.5)(1+cot(kpi/5)), k = m = 1, 2, 3, ..., 9

 

[shaon0]

Thanks untouchablecuz and 3unitz.