17

Part of 2002 India IMO Training Camp

Problems(1)

(1+iT)^n=f(T)+ig(T) where i is the square root of -1

Source: India tst 2002 p17

n

be a positive integer and let

(1+iT)^n=f(T)+ig(T)

i

is the square root of

-1

f

g

are polynomials with real coefficients. Show that for any real number

k

f(T)+kg(T)=0

has only real roots.

algebrapolynomialtrigonometryarithmetic sequencealgebra unsolved