Need Help Part 3 (2 Viewers)

[vivekjain0908]

with part 3 ik we use part ii cube it but idk y im not getting it, can someone1 explain how they wud do it

 

[ExtremelyBoredUser]

Just used the binomial expansion for cubes.

( (e^ix)^3 + 3(e^ix)^2 * (e^-ix) + 3(e^ix) * (e^-ix)^2 (-1)^2 + (-1)^3 * (e^-ix)^3 )

and simplify using index laws:

(e^i3x - (3)(e^i2x*e^-ix) + (3)(e^ix)(e^-i2x) - e^-i3x)

 

[vivekjain0908]

Just used the binomial expansion for cubes.

( (e^ix)^3 + 3(e^ix)^2 * (e^-ix) + 3(e^ix) * (e^-ix)^2 (-1)^2 + (-1)^3 * (e^-ix)^3 )

and simplify using index laws:

(e^i3x - (3)(e^i2x*e^-ix) + (3)(e^ix)(e^-i2x) - e^-i3x)

ah makes sense thx