Предмет: Математика, автор: paygildin02

Найдите,сумму,разность,произведение, частное комплексных чисел z1=1-2i,z2=-1+i

Приложения:

Ответы

Автор ответа: MathDaddy

$z1 = 1 - 2i \\ z2 = - 1 + i$

Сумма:

$z1 + z2 = 1 - 2i - 1 + i = - i$

Разность:

$z1 - z2 = 1 - 2i + 1 - i = 2 - 3i$

Произведение:

$z1 \times z2 = (1 - 2i)( - 1 + i) = \\ = - 1 + i + 2i - 2 {i}^{2} = - 1 + 3i + 2 = \\ = 1 + 3i$

Частное:

$\frac{z1}{z2} = \frac{ 1 - 2i}{ - 1 + i} = \frac{(1 - 2i)( - 1 - i)}{( - 1 + i)( - 1 - i)} = \\ = \frac{ - 1 + 2i - i + 2 {i}^{2} }{1 - i + i - {i}^{2} } = \frac{ - 3 + i}{2} = \\ = - \frac{3}{2} + \frac{1}{2} i = - 1.5 + 0.5i$

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