b=x+yi
b*b=(xi+yj)*(xi+yj)=xi²+xiyj+yj*xi+y²j=1 dar i²=1 j²=1 si i*j=0
b*b=x²+y²=1 rel (1
a*b=(3i-4j)*(xi+yj)=3x-4y=0 (2
Formezi sistem din ecuatia (1 si(2
{x²+y²=1
{3x-4y=0 => y=3x/4 Inlocuiesti in prima ecuatie si obtii
x²+9x²/16=1 => 25x²=16 => x=+/-√16/25=+/-4/5
y=3x/4=+/-3/5
b=4i/5+3j/5 si
b `=-4i/5-3j/5
