Question

Se considera numarul complex z=1+i. Aratati ca z la puterea 2 -2i=0

Answer 1

z^2-2i = (1+i)^2 - 2 i

Din formula (a +b)^2 = a^2+2ab+b^2 deducem ca  z^2=(1+i)^2 = 1^2+2i+i^2

Stim ca i^2 = totdeauna cu -1

=> z^2-2i = 1+2i-1-2i=0