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

$2zw-s^{1023}z$

Realizando las operaciones:

$2zw-s^{1023}z=2\left(-1+2i\right)\left(\sqrt{2}+3i\right)-{\left(-i\right)}^{1023}\left(-1+2i\right)=$

$=\left(-2+4i\right)\left(\sqrt{2}+3i\right)-{\left(-1\right)}^{1023}{i}^{4*255+3}\left(-1+2i\right)=$

$=\left(-2\sqrt{2}-6i+4\sqrt{2}i-12\right)-\left(-1\right)i^3\left(-1+2i\right)=$

$=\left(-2\sqrt{2}-12\right)+i\left(4\sqrt{2}-6\right)-i\left(-1+2i\right)=\left(-10-2\sqrt{2}\right)+i\left(4\sqrt{2}-5\right)$

Cerrar y volver