Question

найти сумму разность произведение и частное комплексных чисел
z1=3+7i z2=2+3i
(Умножение, деление, +, -)

Answer 1

$z_{1} = 3 + 7i \\ z_{2} = 2 + 3i$

1)

$z_{1} + z_{2} = 3 + 7i + 2 + 3i = 5 + 10i$

2)

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

3)

$z_{1}z_{2} = (3 + 7i)(2 + 3i) =3 \times 2 + 3 \times 3i + 7i \times 2+ 7i \times 3i = 6 + 9i + 14i + 21 {i}^{2} = 6 + 23i - 21 = - 15 + 23i$

4)

$\frac{z_{1}}{z_{2}} = \frac{3+ 7i}{2 + 3i} = \frac{(3 + 7i)(2 - 3i)}{(2 + 3i)(2 - 3i)} = \frac{6 - 9i + 14i - 21 {i}^{2} }{ {2}^{2} - 9 {i}^{2} } = \frac{6 +5i + 21}{4 + 9} = \frac{27 +5i}{13} = \frac{27}{13} +\frac{5}{13} i$