Question

Выполните действия. а) z1+z2; б) z1-z2; в)z1*z2; г) z1/z2. Если z1=4+5i и z2=-2+3i

Answer 1

$z_1+z_2=4+5i-2+3i=2+8i\\ z_1-z_2=4+5i+2-3i=6+2i\\ z_1*z_2=(4+5i)(-2+3i)=-8-10i+12i+15i^2=-8-15+2i=\\ =-23+2i\\ \frac{z_1}{z_2} = \frac{4+5i}{-2+3i} = \frac{(4+5i)(-2-3i)}{4+9} = \frac{-8-10i-12i+15}{13} = \frac{7-22i}{13} = \frac{7}{13} - \frac{22}{13} i$