Addizione e sottrazione

$\displaystyle (5+2i)+(-2+i)=5+2i-2+i=3+3i$

$\displaystyle (5+2i)-(-2+i)=5+2i+2-i=7+i$

Moltiplicazione

$\displaystyle (5+2i)\cdot (-2+i)=-10-4i+5i+2i^2=-10-4i+5i-2==-12+i$

Reciproco

$z=2-3i$, il reciproco di $z$ é:

$\displaystyle\frac{1}{z}=\frac{1}{2-3i}=\frac{1}{2-3i}\cdot \frac{2+3i}{2+3i}=\frac{2+3i}{4-9i^2}=\frac{2+3i}{4+9}=\frac{2+3i}{13}=\frac{2}{13}+\frac{3}{13}i$

Divisione

$\displaystyle\frac{1+i}{2-3i}= \frac{1+i}{2-3i}\cdot \frac{2+3i}{2+3i}=\frac{2+3i+2i+3i^2}{4+9}=\frac{2+3i+2i-3}{13}=\frac{-1+5i}{13}$

$\displaystyle =\frac{-1}{13}+\frac{5}{13}i$