Question

Комплексные числа
((1+i)^3 -1)/((1-i)^3 +1)​

Answer 1

$\frac{(1+i)^{3}-1 }{(1-i)^{3} +1}=\frac{1^{3}+3*1^{2}*i+3*1*i^{2}+i^{3}-1}{1^{3}-3*1^{2}*i+3*1*i^{2}-i^{3}+1}=\frac{1+3i-3-i-1}{1-3i-3+i+1}=\frac{2i-3}{-2i-1}=\frac{3-2i}{1+2i}=\frac{(3-2i)(1-2i)}{(1+2i)(1-2i)}=\frac{3-6i-2i+4i^{2} }{1-4i^{2} }=\frac{3-8i-4}{1+4}=-\frac{1+8i}{5}$

Answer 2

$\frac{(1+i)^{3}-1 }{(1-i)^{3} +1}=\frac{1^3+3\cdot1^{2}\cdoti+3\cdot1\cdoti^2+i^3-1}{1^3-3\cdot1^2\cdot i+3\cdot1\cdo ti^2-i^{3}+1}=\frac{1+3i-3-i-1}{1-3i-3+i+1}=\\\\\frac{2i-3}{-2i-1}=\frac{3-2i}{1+2i}=\frac{(3-2i)(1-2i)}{(1+2i)(1-2i)}=\frac{3-6i-2i+4\cdot i^2}{1-4i^2}=\\\\\frac{-8i+3+4 \cdot(-1)}{1-4\cdot(-1)}=\frac{-8i+3-4}{1+4}=\frac{-8i-1}{5}$