Question

Sa se afle numerele reale x si y,stiind ca:
(2x+yi)-(y+3xi)=3-5i

Answer 1

(2x+yi)-(y+3xi) = 3 - 5i
(2x+y)-(3xi+yi) = 3 - 5i
(2x+y)-(3x+y)i = 3 - 5i
$\left \{ {{2x + y = 3} \atop {3x+y=5}} \right.$
2x = 3 - y ⇔ x = $\frac{3-y}{2}$
Inlocuind, avem:
$3 \frac{3-y}{2} +y=5$ ⇔ $\frac{9-3y}{2} + \frac{2y}{2} = \frac{10}{2}$ ⇔ 9 - 3y + 2y = 10 ⇔ 9 - y = 10 ⇔ -y = 10 - 9 ⇔ y = -1.
Inlocuind, avem:
2x - 1 = 3 ⇔ 2x = 4 ⇔ x = 2.