Question

Задание 4. Выполнить деление комплексных чисел:
Z1 = 6+i, Z2 = 1+ 2i
Z1 = -2 + 2i, z, = 1 + Зі
Z1 = 4 +i, z = -1 + 6i
Z1 = -1 + 5i, z = 2 +і

Answer 1

1)

$\displaystyle \frac{6+i}{1+2i}=\frac{(6+i)*(1-2i)}{1^2-(2i)^2}=\frac{6+i-12i-2i^2}{1-4i^2}=\frac{6-11i+2}{1+4}=\frac{8-11i}{5}$

2)

$\displaystyle\frac{-2+2i}{1+3i}=\frac{(-2+2i)(1-3i)}{1^2-(3i)^2}=\frac{-2+2i+6i-6i^2}{1+9}=\frac{4+8i}{10}=0.4+0.8i$

3)

$\displaystyle\frac{4+i}{-(1-6i)}= \frac{(4+i)(1+6i)}{-(1^2-(6i)^2)}=\frac{4+i+24i+6i^2}{-37}=\frac{-2+25i}{-37}$

4)

$\displaystyle\frac{-1+5i}{2+i}=\frac{(-1+5i)(2-i)}{(4-i^2)}=\frac{-2+10i+i-5i^2}{5}=\frac{3+11i}{5}$