Complex numbers

If x1,x2...xn are roots of equation xn+p1xn-1+p2xn-2+...+pn-1x+pn=0 where p1,p2..pn real,
Prove that(1+x12)(1+x22)(1+x32)..(1+xn2)=(1-p2+p4-p6+...)2+(p1-p3+p5-....)2

1 Answers

341
Hari Shankar ·

Let f(x) = xn+p1xn-1+...+pn

Then the given expression = |f(i)|

Your Answer

Close [X]