Question

Dados los siguientes números complejos:

A = -3 – 5i B = 6 + 9i C = -8 + 3i D = -3 + i

Hallar:
1. A + D

2. C – D

3. (A x C) + ( A x C)

4. BD

Answer 1

Explicación paso a paso:

$a + d = ( - 3 - 5i) + ( - 3 + i) = - 3 - 5i - 3 + i = - 6 - 4i$

$c - d = ( - 8 + 3i) - ( - 3 + i) = - 8 + 3i + 3 - i = - 5 + 2i$

$(a \times c) + (a \times c) = ( - 3 - 5i)( - 8 + 3i) + ( - 3 - 5i)( - 8 + 3i) = 24 - 9i + 40i - 15 {i}^{2} + (24 - 9i + 40i - 15 {i}^{2} ) = 24 - 9i + 40i- 15 {i}^{2} + 24 - 9i + 40i - 15 {i}^{2} = 48 - 18i + 80i - 30 {i}^{2} = 48 + 62i - 30( - 1) = 48 + 62i + 30 = 78 + 62i$

$bd = (6 + 9i)( - 3 + i) = - 18 + 6i - 27i + 9 {i}^{2} = - 18 - 21i + 9( - 1) = - 18 - 21i - 9 = - 27 - 21i$