Ejercicio

Dados los números complejos:

$\begin{array}{lllll}z=-1+2i\hfill & ,\hfill & w=\sqrt{2}+3i\hfill & ,\hfill & s=-i\hfill \end{array}$

Realice la siguiente operación

$s^{1023}+s^{1024}+s^{1025}+s^{1026}$

Se tiene que:

$\begin{array}{c}{s}^{1023}={\left(-i\right)}^{1023}={\left(-1\right)}^{1023}{\left(i\right)}^{4*255+3}=\left(-1\right)i^3=i\\ s^{1024}={\left(-i\right)}^{1024}={\left(-1\right)}^{1024}{\left(i\right)}^{4*256+0}=i^0=1\\ s^{1025}={\left(-i\right)}^{1025}={\left(-1\right)}^{1025}{\left(i\right)}^{4*256+1}=\left(-1\right)i^1=-i\\ s^{1026}={\left(-i\right)}^{1026}={\left(-1\right)}^{1026}{\left(i\right)}^{4*256+2}=i^2=-1\end{array}$

Por lo tanto la suma vale 0.

Cerrar y volver