Задача 52431 Помогите Пожалуйста...

vk477579336

2020-06-14 18:31:08

Помогите Пожалуйста

sova

2020-06-14 21:07:36

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z_(1)=x_(1)+iy_(1) ⇒ vector{z_(1)}=x_(1)-iy_(1)
z_(2)=x_(2)+iy_(2) ⇒ vector{z_(2)}=x_(2)-iy_(2)

a)
z_(1)+z_(2)=x_(1)+x_(2)+i*(y_(1)+y_(2))

vector{z_(1)+z_(2)}=[b]x_(1)+x_(2)-i*(y_(1)+y_(2))[/b]


vector{z_(1)}+vector{z_(2)}=x_(1)-iy_(1)+x_(2)-iy_(2)=[b]x_(1)+x_(2)-i*(y_(1)+y_(2)) [/b]⇒

vector{z_(1)+z_(2)}=vector{z_(1)}+vector{z_(2)}


б)
z_(1)*z_(2)=(x_(1)+iy_(1))*(x_(2)+iy_(2) )= x_(1)*x_(2)-y_(1)y_(2)+i*(y_(1)x_(2)+y_(2)x_(1))=


vector{z_(1)*z_(2)}=[b]x_(1)*x_(2)-y_(1)y_(2)-i*(y_(1)x_(2)+y_(2)x_(1))[/b]

vector{z_(1)}*vector{z_(2)}=(x_(1)-iy_(1))*(x_(2)-iy_(2))=[b]x_(1)x_(2)-y_(1)y_(2)-i*(y_(1)x_(2)+y_(2)x_(1)[/b]

⇒ vector{z_(1)*z_(2)}=vector{z_(1)}*vector{z_(2)}