Let m1(t) and m2(t) be message signals and let s1(t) and s2(t) be the corresponding modulated signals using a carrier frequency of fc.

a. Show that if simple AM modulation is used, then m1(t) + m2(t) produces a modulated signal equal that is a linear combination of s1(t) and s2(t). This is why AM is sometimes referred to as linear modulation.

b. Show that if simple PM modulation is used, then m1(t) + m2(t) produces a modulated signal that is not a linear combination of s1(t) and s2(t). This is why angle modulation is sometimes referred to as nonlinear modulation.