Question

Помогите решить комплексные числа
z1=4-9i
z2=-3+6i
решить с +,-,*,÷​​

Answer 1

$z_{1} = 4 - 9i \\ z_{2} = - 3 + 6i$

1)

$z_{1} + z_{2} = 4 - 9i + ( - 3 + 6i) = 4 -9i - 3 + 6i = 1 - 3i$

2)

$z_{1} - z_{2} = 4 - 9i - ( - 3 + 6i) = 4 - 9i + 3 - 6i = 7 - 15i$

3)

$z_{1}z_{2} = - (4 - 9i)(3 - 6i) = - (12 - 24i - 27i + 54 {i}^{2} ) = - (12 - 51i - 54) = - ( - 42 - 51i) = 42 + 51i$

4)

$\frac{z_{1}}{z_{2}} = \frac{4 - 9i}{ - 3 + 6i} = - \frac{4 - 9i}{3 - 6i} = - \frac{(4 - 9i)(3 + 6i)}{(3 - 6i)(3 + 6i)} = - \frac{12 + 24i - 27i - 54 {i}^{2} }{ {3}^{2} - (6i) {}^{2} } = - \frac{12 - 3i + 54}{9 + 36} = - \frac{66 - 3i}{45} = - \frac{22 - i}{15} = - \frac{22}{15} + \frac{1}{15} i$