YBK
w00t! custom status!! :D
hey, any help on this question would be greatly appreciated
I can do the first part, but not the second.
Let F(z) = z^8 - 7/3 z^4 + 1
The complex number a is a root of F(z) = 0
i) Show that Ia and 1/a are also roots of F(z) = 0
a^8 - 7/3 a^4 + 1 = 0
(Ia)^8 - 7/3 (Ia)^4 + 1
= a^8 - 7/3a^4 + 1
=0
(1/a)^8 - 7/3 (1/a)^4 + 1
= {1 + 7/3 a^4 + a^8}/a^8
= 0
ii) Find all the roots of P(z) = 0
Can't get far with this part.
Thanks
I can do the first part, but not the second.
Let F(z) = z^8 - 7/3 z^4 + 1
The complex number a is a root of F(z) = 0
i) Show that Ia and 1/a are also roots of F(z) = 0
a^8 - 7/3 a^4 + 1 = 0
(Ia)^8 - 7/3 (Ia)^4 + 1
= a^8 - 7/3a^4 + 1
=0
(1/a)^8 - 7/3 (1/a)^4 + 1
= {1 + 7/3 a^4 + a^8}/a^8
= 0
ii) Find all the roots of P(z) = 0
Can't get far with this part.
Thanks