z=x+iy
|z|=√(x²+y²)
cosφ=x/|z|
sinφ=y/|z|
z=-1+√3i
x=-1; y=√3
|z|=√((-1)²+(√3)²)=2
cosφ=x/|z|=-1/2
sinφ=y/|z|=√3/2
φ=2π/3
Тригонометрическая форма:
z=2(cos(2π/3)+isin(2π/3))
z⁵=2⁵(cos5·(2π/3)+isin5·(2π/3))=32(cos(10π/3)+isin(10π/3))=
=32(cos(4π-(2π/3))+isin(4π-(2π/3))=
=32(cos(-(2π/3))+isin(-(2π/3))=
=32(cos(2π/3)-isin(2π/3)=32(1-√3i)
О т в е т. 1-√3i
