My question is when we use this theorem

z=4(cos60+isin60) * 4(cos 60 +i sin 60)

z^2= 16 (cos 120 +isin 120) *4(cos 60 +i sin 60)

z^3= 64 (cos 180 + i sin 180)

Why do we just add the 60 degrees to each

why do we not distribute? to get 16+ 8 cos 60 +8 i sin 60 + cos 60^2 + (i sin 60)^2

if that is correct how does that become line 2? thanks

Do we add the values because of the sum and difference formulas?