Question

Se considera numarul complex z=-1+i rad din 3 totul supra 2.Sa se demonstreze ca z^2=z

Answer 1

$z= \frac{-1+i \sqrt{3} }{2} \\ z^2= \frac{(i \sqrt{3}-1)^2}{4} = \frac{-3-2i \sqrt{3} +1}{4}= \\ = \frac{-4-2i \sqrt{3} }{4}= \frac{-1-i \sqrt{3} }{2}=\~z$