Question

Son la potencia de i ​

Answer 1

Respuesta:

-7 + 7i

Explicación paso a paso:

Se cumple:

$i = \sqrt{ - 1}$

${i}^{2} = - 1$

${i}^{3} = - i$

${i}^{4} = 1$

${i}^{4k} = 1$

${i}^{4k + m} = {i}^{m}$

Entonces:

$4 {i}^{6} + 8 {i}^{9} - 2 {i}^{20} - ( {i}^{16} + {i}^{33} )$

$4 {i}^{4 + 2} + 8 {i}^{4(2) + 1} - 2 {i}^{4(5)+0} - ( {i}^{4(4)+0} + {i}^{4(8) + 1})$

$4 {i}^{ 2} + 8 {i}^{1} - 2 {i}^{0} - ( {i}^{0} + {i}^{1})$

$4( - 1) + 8i - 2(1) - ( 1 + i)$

$- 4 + 8i - 2- ( 1 + i)$

$- 6 + 8i - ( 1 + i)$

$- 6 + 8i - 1 - i$

$- 7 + 7i$