Question

sa se calculeze z+1\z pt z= (--1+i radical3) \2

Answer 1

z= (--1+i radical3) \2 este solutie a ecuatiei z²+z+1=0
z+1\z =(z²+1)/z=-z/z=-1

Answer 2

[tex]\it z = \dfrac{-1+i\sqrt3}{2} \\\;\\ \\\;\\ \dfrac{1}{z} = \dfrac{2}{-1+i\sqrt3} = \dfrac{2(-1-i\sqrt3)}{(-1)^2-(i\sqrt3)^2} =\dfrac{2(-1-i\sqrt3)}{1 +3} = \\\;\\ \\\;\\ =\dfrac{2(-1-i\sqrt3)}{4} = \dfrac{-1-i\sqrt3}{2} [/tex]


[tex]\it z+\dfrac{1}{z} = \dfrac{-1+i\sqrt3}{2} + \dfrac{-1-i\sqrt3}{2} = \dfrac{-1+i\sqrt3-1-i\sqrt3}{2} = \\\;\\ \\\;\\ = \dfrac{-2}{2}=-1.[/tex]