Question

Найти мнимую часть комплексного числа: z=1+i / 1-3i

Answer 1

$\dfrac{1+i}{1-3i}=\dfrac{(1+i)(1+3i)}{(1-3i)(1+3i)}=\dfrac{-2+4i}{10}=-0.2+0.4i\\ \mathop{\mathrm{Im}}\left(\dfrac{1+i}{1-3i}\right)=\mathop{\mathrm{Im}}\left(-0.2+0.4i\right)=0.4$