Question

Даны 2 комплексных числа z1=2+5i ; z2=3-6i. Вычислите: z1+z2; z1-z2; z1*z2; z1:z2

Answer 1

$\boxed {\ \ i^2=-1\ \ }$

$z_1=2+5i\ \ ,\ \ \ z_2=3-6i\\\\z_1+z_2=(2+5i)+(3-6i)=(2+3)+(5i-6i)=5-i\\\\z_1=z_2=(2+5i)-(3-6i)=(2-3)+(5i+6i)=-1+11i\\\\z_1\cdot z_2=(2+5i)\cdot (3-6i)=6-12i+15i-30i^2=6+3ii+30=36+3i$

$\dfrac{z_1}{z_2}=\dfrac{2+5i}{3-6i}=\dfrac{(2+5i)(3+6i)}{(3-6i)(3+6i)}=\dfrac{6+12i+15i+30i^2}{9-36i^2}=\dfrac{6+27i-30}{9+36}=\\\\\\=\dfrac{-24+27i}{45}=-\dfrac{24}{45}+\dfrac{27}{45}\, i$