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

$\frac{1}{2}z-\frac{3}{5}\overline{w}\mathrm{Im}\left(s\right)+szw$

Sustituyendo en la expresión a calcular

$\frac{1}{2}z-\frac{3}{5}\overline{w}\mathrm{Im}\left(s\right)+szw=\frac{1}{2}\left(-1+2i\right)-\frac{3}{5}\overline{\left(\sqrt{2}+3i\right)}\mathrm{Im}\left(-i\right)+\left(-i\right)\left(-1+2i\right)\left(\sqrt{2}+3i\right)=$

$=\left(\frac{-1}{2}+i\right)-\frac{3}{5}\left(\sqrt{2}-3i\right)\left(-1\right)+\left(i+2\right)\left(\sqrt{2}+3i\right)=$

$=\left(\frac{-1}{2}+i\right)+\left(\frac{3\sqrt{2}}{5}-\frac{9}{5}i\right)+\left(2\sqrt{2}-3+\sqrt{2}i+6i\right)=$

$=\frac{-5+6\sqrt{2}+20\sqrt{2}-30}{10}+i\frac{5-9+5\sqrt{2}+30}{5}=\frac{-35+26\sqrt{2}}{10}+i\frac{26+5\sqrt{2}}{5}$

Cerrar y volver