Question

Determine  $(-1)^{ \sqrt{2}}$. Dica: Numeros Complexos

Answer 1

Caso tenha problemas para visualizar a resposta, experimente abrir pelo navegador:  https://brainly.com.br/tarefa/8121948

_______________


$\mathsf{(-1)^{\sqrt{2}}}\\\\ =\mathsf{(-1+0i)^{\sqrt{2}}}\\\\ =\mathsf{(cos\,\pi+i\cdot sen\,\pi)^{\sqrt{2}}}\\\\ =\mathsf{\big(e^{\hspace{-4}\begin{array}{l}\mathsf{i\cdot \pi}\end{array}\hspace{-5}}\big)^{\sqrt{2}}}\\\\ =\mathsf{e^{\hspace{-4}\begin{array}{l}\mathsf{i\cdot \pi}\end{array}\hspace{-5}\sqrt{2}}}$

$=\mathsf{cos(\pi\sqrt{2})+i\cdot sen(\pi \sqrt{2})}\\\\ \approx \mathsf{-0,\¨266-0,\¨964\,i\qquad\quad\checkmark}$


Bons estudos! :-)


Tags:  exponencial potência número complexo