Complex numbers - Root of unity (1 Viewer)

[HeroicPandas]

If α is a complex root of z⁷-1=0, show that:

a) α³ is also a complex root and hence state all the complex roots of z⁷-1=0 in terms of α. (answer = α, α², α³,α⁴,α⁵,α⁶)

b) The quadratic equation whose roots are α+α²+α⁴ and α³+α⁵+α⁶ is z²+z+2=0

ok i've done part a, but part b the only thing i can think of doing is the long way...sub in the roots to the equation and it works, but thats the stupidest way in the world

 

[HeroicPandas]

this isnt a joke, i really need help

 

[umm what]

If α is a complex root of z⁷-1=0, show that:

a) α³ is also a complex root and hence state all the complex roots of z⁷-1=0 in terms of α. (answer = α, α², α³,α⁴,α⁵,α⁶)

b) The quadratic equation whose roots are α+α²+α⁴ and α³+α⁵+α⁶ is z²+z+2=0

ok i've done part a, but part b the only thing i can think of doing is the long way...sub in the roots to the equation and it works, but thats the stupidest way in the world

is it?

 

[math man]

For part b work out the sum of those
Two and then the product and then sub
Those numbers into standard form of
A quadratic and you will get answer

 

[umm what]

I have seen this question is Excel S.K Patel ... they use "the stupidest way in the world" to solve it

 

[HeroicPandas]

i have seen this question is excel s.k patel ... They use "the stupidest way in the world" to solve it

hahahahahahaaha loooooooooooool,

 

[umm what]

hahahahahahaaha loooooooooooool,

No jks

 

[HeroicPandas]

For part b work out the sum of those
Two and then the product and then sub
Those numbers into standard form of
A quadratic and you will get answer

\

so blah blah = -b (SUM)

blah blah = c (PRODUCT)

OR

blah blah = -1 (SUM)

blah blah = 2 (PRODUCT)

 

[HeroicPandas]

For part b work out the sum of those
Two and then the product and then sub
Those numbers into standard form of
A quadratic and you will get answer

i've done this way but i get α+.......+α^6 = -b

α+.......+α^6 = c

where a^7 = 1

 

[math man]

 

[HeroicPandas]

View attachment 26129

thanks math man, i knew i was doing it right, i just forgot to put it back in quadratic form lol