please answer des doubts

1 + 2mcosx + m^{2} = (1 + me^{ix}) (1 + me^{-ix}) = 1 + m^{2} + m(e^{ix} + e^{-ix})
now use Euler's formula e^{ix} = cosx + isinx

so e^{ix} = cosx + isinx .....e^{-ix} = cosx - isinx......e^{ix} + e^{-ix} = 2cosx

how it changes when m> 1 and when 0< m< 1

plz xplain

-1 < real|e^{ix}| < 1 ....maybe bcoz of this there is a change at m = 1

plz can anyone explain this