Question

Комплексные числа! Найти:

Answer 1

$frac{(2+3i)(5-i)}{2+i}= frac{10+15i-2i-3i^2}{2+i}= frac{10+13i+3}{2+i}= frac{13+13i}{2+i}= frac{(13+13i)(2-i)}{(2+i)(2-i)}=\\= frac{26+26i-13i-13i^2}{4-i^2}= frac{26+13i+13}{4+1}= frac{39+13i}{5}=7,8+2,6i$

$(2i-1)^4-((2i+1)^4=((2i-1)^2+(2i+1)^2)((2i-1)^2-(2i+1)^2)=\\=(4i^2-4i+1+4i^2+4i+1)(4i^2-4i+1-4i^2-4i-1)=\\=(-4-4+2)(-8i)=-6*(-8i)=48i$