Question

Помогите пожалуйста решить!

Answer 1

$\displaystyle z_1= -2+3i; z_2=4+5i\\\\z_1+z_2=-2+3i+4+5i=(-2+4)+(3i+5i)=2+8i$

$\displaystyle z_1-2z_2=(-2+3i)-2(4+5i)=-2+3i-8-10i=(-2-8)+(3i-10i)=\\\\=-10-7i$

$\displaystyle z_1*z_2=(-2+3i)(4+5i)=-8+12i-10i+15i^2=(-8+15i^2)+(12i-10i)=\\\\=(-8-15)+2i=-23+2i$

$\displaystyle\frac{z_1}{z_2}=\frac{(-2+3i)}{(4+5i)}=\frac{(-2+3i)(4-5i)}{4^2-(5i)^2}=\frac{-8+12i+10i-15i^2}{16+25}=\frac{7+22i}{41}$