Question

ПОМОГИТЕ РЕШИТЬ КОМПЛЕКСНЫЙ ЧИСЛА

Answer 1

$(sqrt{3}-i)^{20}=(2*(frac{sqrt 3}{2}-i*frac{1}{2}))^{20}=\\=2^{20}*(cos (-frac{pi}{6})+i*sin(-frac{pi}{6}))^{20}=\\=2^{20}*(cos(-frac{10pi}{3})+i*sin(-frac{10pi}{3}))=\\=2^{20}*(cos(frac{2pi}{3})+i*sin(frac{2pi}{3}));$

$(1+i)^{15}=(sqrt 2*(frac{sqrt 2}{2}+ i*frac{sqrt 2}{2}))^{15}=\\=(sqrt 2)^{15}*(cos(frac{pi}{4})+i*sin(frac{pi}{4}))^{15}=\\=2^{frac{15}{2}}*(cos(frac{15pi}{4})+i*sin(frac{15pi}{4}))=\\=2^{7.5}*(cos(-frac{pi}{4})+i*sin(-frac{pi}{4}));$

$(sqrt 3 -i)^{20}(1+i)^{15}=\\=2^{20}*(cos(frac{2pi}{3})+i*sin(frac{2pi}{3}))*2^{7.5}*(cos(-frac{pi}{4})+i*sin(-frac{pi}{4}))=\\=2^{27.5}*(cos(frac{5pi}{12})+i*sin(frac{5pi}{12}))=\\=2^{26.5}*sqrt{2-sqrt 3}+i*2^{26.5}*sqrt{2+sqrt 3}$