Question

Предмет алгебра теория чисел. Комплексные числа

Answer 1

1.

$z^2+2z-(2+4i)=0$

$z_1=-1+\sqrt{1+2+4i} =-1+\sqrt{(2+i)^2} =1+i$

$z_2=-1-\sqrt{1+2+4i} =-1-\sqrt{(2+i)^2} =-3-i$

2.

$\sqrt[5]{\frac{(1-\sqrt{3}i)(1+i) }{\sqrt{3} -i} } =\sqrt[5]{-1+i} =\sqrt[5]{\sqrt{2}(cos\frac{3\pi}{4} +isin\frac{3\pi}{4})} =(\sqrt{2}e^\frac{3i\pi}{4})^{\frac{1}{5}}=\sqrt[10]{2}e^\frac{3i\pi}{20}=\sqrt[10]{2}(cos\frac{3\pi}{20} +isin\frac{3\pi}{20})$