(3/2-корень 3/2і)^6/6× е^-і п/3

Question

(3/2-корень 3/2і)^6/6× е^-і п/3

Answer 1

A⁶/6b

a = 3/2 - i√3/2

|a| = √(9/4 + 3/4) = √(12/4) = √3

a = √3(cos(π/6) - i*sin(π/6)) = √3e^(-iπ/6)

a⁶ = 27e^(-iπ)

a⁶/6b = 27e^(-iπ)/(6e^(-iπ/3)) = 4,5e^(-2πi/3)

Ответ: 4,5e^(-2πi/3)