Question

Z1=5+i z2=4-2i найти z1+z2,z1-z2,z1*z2,z1/z2

помагите даю 20 бал

Answer 1

$z_1 = 5 + i$

$z_2 = 4 - 2i$

$z_1 + z_2 = 5+i + 4 - 2i = 5+4 + i - 2i = 9 - i$

$z_1 - z_2 = 5+i - (4 - 2i) = 5+i - 4 + 2i = 5-4 + i + 2i = 1 + 3i$

$z_1\cdot z_2 = (5+i)\cdot (4 - 2i) = 5\cdot 4 + 5\cdot(-2i) + i\cdot 4 + i\cdot (-2i) =$

$= 20 - 10i + 4i - 2i^2 = 20 - 6i - 2\cdot(-1) = 20 + 2 - 6i = 22 - 6i$

$\frac{z_1}{z_2} = \frac{5+i}{4-2i} = \frac{(5+i)\cdot(4+2i)}{(4-2i)\cdot(4+2i)} =$

$= \frac{5\cdot 4 + 5\cdot 2i + i\cdot 4 + i\cdot 2i}{4\cdot 4 + 4\cdot 2i -2i\cdot 4 -2i\cdot 2i} =$

$= \frac{20 + 10i + 4i + 2i^2}{16 + 8i - 8i -4i^2} =$

$= \frac{20 + 14i + 2\cdot(-1)}{16 - 4\cdot(-1)} =$

$= \frac{20 - 2 + 14i}{16 + 4} = \frac{18 + 14i}{20} =$

$= \frac{18}{20} + \frac{14}{20}\cdot i = \frac{9}{10} + \frac{7}{10}\cdot i =$

$= 0{,}9 + 0{,}7i$