Complex number question (1 Viewer)

[cutemouse]

Hello,

I haven't come across this one before, except in this year's Ext 2 trial for my school. I have no idea on how to solve it. Could someone please help me out?

If ω is a non real solution to z⁶=1, show that ω⁶+ω⁴=-1

Thanks

 

[azureus88]

interesting....but it doesnt seem rite cause w^6 + w^4 = -1 gives w^4 = -2 and LHS is not real. Unless w isnt complex root of unity with smallets argument...

 

[DkAssain]

easy wuestions i try tomz
cant be bothered
looks interesting

 

[gurmies]

I've made the same observation as azureus88, and am not sure how to interpret this anomalistic result. Seems incorrect to me..

 

[cutemouse]

Hi guys,

I actually posted one part of the question by mistake, here is the whole question:

a) Find all the solutions to the equation z⁶=1 in the form of x+iy
b) If ω is a non real solution to z⁶=1, show that ω⁶+ω⁴=-1 [as above]
c) By choosing one particular value of ω, explain with the aid of a diagram why ω⁶+ω⁴=-1

 

[cutemouse]

Ahh, I think I know how to do this now!!

Thanks everyone.

 

[azureus88]

no worries, glad i helped! lol