Anyone would like to try to work out and explain these root of unity questions?
1. Let w, a complex number, be the cube root of unity.
(a) find possible values of w.
(b) Show w^2 + w + 1 = 0
(c) Hence simplify, (1+w)^6
2. Given w, a complex number, is a root of equation z^3-1=0, find:
(a) a+bw+cw^2 / c + aw + bw^2
(b) (1-w+w^2)(1+w-w^2)
3. A polynomial R(z) is given by R(z) = z^6 -1. Let (alpha) not = to 1, be that complex root of R(z) =0 which has the smallest positive argument. Show that 1+(alpha)+(alpha)^2 + (alpha)^3....(alpha)^5 = 0.
1. Let w, a complex number, be the cube root of unity.
(a) find possible values of w.
(b) Show w^2 + w + 1 = 0
(c) Hence simplify, (1+w)^6
2. Given w, a complex number, is a root of equation z^3-1=0, find:
(a) a+bw+cw^2 / c + aw + bw^2
(b) (1-w+w^2)(1+w-w^2)
3. A polynomial R(z) is given by R(z) = z^6 -1. Let (alpha) not = to 1, be that complex root of R(z) =0 which has the smallest positive argument. Show that 1+(alpha)+(alpha)^2 + (alpha)^3....(alpha)^5 = 0.