Osnovne operacije s kompleksnim brojevima

Izračunajte $z_1+z_2,\, z_1-z_2,\, z_1\cdot z_2$ i $\displaystyle\frac{z_1}{z_2}$ ako je $z_1=1-i,\, z_2=2+3i$ .

Rješenje. Vrijedi

	$\displaystyle z_1+z_2=(1-i)+(2+3i)=3+2i,$
	$\displaystyle z_1-z_2=(1-i)-(2+3i)=-1-4i,$
	$\displaystyle z_1\cdot z_2=(1-i)\cdot(2+3i)=2+3i-2i-3i^2=5+i,$
	$\displaystyle \frac{z_1}{z_2}=\frac{1-i}{2+3i}\cdot\frac{2-3i}{2-3i}=\frac{2-3i-2i+3i^2}{2^2-(3i)^2}=\frac{-1-5i}{4+9}=-\frac{1}{13}-\frac{5}{13}\,i.$