Răspuns:
nu sunt coliniare
Explicație pas cu pas:
[tex] Conditia \ de \ coliniaritate \ a \ trei \ puncte \ in \ plan:\\ \\ A(a), \ B(b) \ si \ C(c) \ sunt \ coliniare \ daca \ \frac{b-a}{c-a}\in \mathbb{R^*}[/tex]
[tex] a) \ A, \ B, \ C \ sunt \ coliniare \ daca \ \frac{b-a}{c-a}\in \mathbb{R^*}, \\ \\ unde \ a=3, \ b=1+i \ si \ c=-1+\frac{5}{2}i\\ \\ \ \frac{1+i-3}{-1+\frac{5}{2}i-3}=[/tex]
[tex]= \frac{-2+i}{-4+\frac{5}{2}i}= \frac{-2+i}{\frac{-8}{2}+\frac{5i}{2}}=\\ \\ =\frac{-2+i}{\frac{-8+5i}{2}} =\frac{(-2+i)\cdot 2}{-8+5i}=\\ \\= \frac{-4+2i}{-8+5i}=\\ \\ (amplificam \ cu \ conjugatul \ numitorului)[/tex]
[tex]=\frac{(-4+2i)(-8-5i)}{(-8+5i)(-8-5i)}=\\ \\ =\frac{32+20i-16i-10i^2}{(-8)^2-(5i)^2}=\\ \\ =\frac{32+4i+10}{64+25}=\\ \\ =\frac{42+4i}{89} \not{\in} \mathbb{R^*}[/tex]
