Question

обчислити (1+і√3)^10

Answer 1

z=1+i√3
|z|=√(1+3)=√4=2
argφ=arctg√3
φ=π/3
z=2(cosπ/3+isinπ/3)
$(1+i sqrt{3} ) ^{10} =2 ^{10} (cos(10* pi /3)+isin(10* pi /3)=$$2 ^{10} (cos4 pi /3+isin 4 pi /3)=2 ^{10} (-1/2-i sqrt{3} /2)$