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

Source: India tst 2002 p17

July 13, 2012

algebrapolynomialtrigonometryarithmetic sequencealgebra unsolved

Problem Statement

Let

n

be a positive integer and let

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

where

i

is the square root of

-1

, and

f

and

g

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

k

the equation

f(T)+kg(T)=0

has only real roots.