Variable Compleja (inverso aditivo)Usa i = (0, 1) y y = (y, 0) para verificar que - (iy) = ( - i)y?

Recordemos los siguiente<img src="https://tex.z-dn.net/?f=%28a_1%2Cb_1%29%5Ccdot%20%28a_2%2Cb_2%29%3D%28a_1a_2-b_1b_2%2Ca_1b_2%2Ba_2b_1%29" />

Luego se tiene

<img src="https://tex.z-dn.net/?f=-%28iy%29%3D-%5B%280%2C1%29%5Ccdot%28y%2C0%29%5D%3D-%280%2Cy%29%20%3D%20%280%2C-y%29%5C%5C%0A%28-i%29y%3D%280%2C-1%29%5Ccdot%28y%2C0%29%3D%280%2C-y%29%5C%5C%20%5C%5C%0A%5CLongrightarrow%20-%28iy%29%3D%28-i%29y" /> = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

Luego<img src="https://tex.z-dn.net/?f=%28-i%29y%2B%28iy%29%3D0" />.

También<img src="https://tex.z-dn.net/?f=%28-x%29%2Bx%3D0" />

<img src="https://tex.z-dn.net/?f=%5B%28-i%29y%2B%28iy%29%5D%2B%5B%28-x%29%2Bx%5D%3D0%2B0i%5C%5C%20%5C%5C%20%0A%5Cleft%5B%28-i%29y%2B%28iy%29%5Cright%5D%2B%5Bx%2B%28-x%29%5D%3D%5Cmathbf0%5C%5C%20%20%5C%5C%0A%28-i%29y%2B%5B%28iy%29%2Bx%5D%2B%28-x%29%3D%5Cmathbf0%5C%5C%20%5C%5C%0A%28-i%29y%2B%28-x%29%2B%5B%28iy%29%2Bx%5D%3D%5Cmathbf0%5C%5C%5C%5C%0A%5Cleft%5B%28-i%29y%2B%28-x%29%5Cright%5D%2B%5B%28iy%29%2Bx%5D%3D%5Cmathbf0%5C%5C%20%5C%5C%0A%5Cleft%5B%28-x%29%2B%28-i%29y%5Cright%5D%2B%5Bx%2B%28iy%29%5D%3D%5Cmathbf0%5C%5C%20%5C%5C%0A%5Cleft%5B%28-x%29-%28iy%29%5Cright%5D%2B%5Bx%2B%28iy%29%5D%3D%5Cmathbf0%5C%5C%20%5C%5C%0A%5Ctext%7BPor%20ende%20el%20inverso%20aditivo%20de%20%7Dz%5Ctext%7B%20es%20%7D%28-x%29-%28iy%29%3D-x-iy%3D-z" />.