Can someone please show me how to do this question from the Cambridge book?
a) Use De Moivre's theorem to solve z^5 =-1.
[I can do this part; z= -1, cis(+)(-) pi/5, cis(+)(-) (3pi)/5; (+)(-)= plus or minus]
This is the part I don't get at all:
b) By grouping the roots in complex conjugate pairs, show that
z^5 + 1 = (z+1)(z^2 - 2z (cos pi/5) + 1)(z^2 - 2z (cos 3pi/5) +1)
a) Use De Moivre's theorem to solve z^5 =-1.
[I can do this part; z= -1, cis(+)(-) pi/5, cis(+)(-) (3pi)/5; (+)(-)= plus or minus]
This is the part I don't get at all:
b) By grouping the roots in complex conjugate pairs, show that
z^5 + 1 = (z+1)(z^2 - 2z (cos pi/5) + 1)(z^2 - 2z (cos 3pi/5) +1)