Question

Z1=3+7i Z2=1-4i найти Z1+Z2 Z1-Z2 Z1×Z2 Z1/Z2​

Answer 1

Ответ:

$z_1=3+7i\ \ ,\ \ \ z_2=1-4i\\\\z_1+z_2=(3+1)+(7-4)i=4+3i\\\\z_1-z_2=(3-1)+(7+4)i=2+11i\\\\z_1\cdot z_2=(3+7i)\cdot (1-4i)=3-12i+7i-28i^2=31-5i\\\\\dfrac{z_1}{z_2}=\dfrac{3+7i}{1-4i}=\dfrac{(3+7i)(1+4i)}{(1-4i)(1+4i)}=\dfrac{3+12i+7i+28i^2}{1-16i^2}=\dfrac{-25+19i}{17}=\\\\\\=-\dfrac{25}{17}+\dfrac{19}{17}\, i$