Possible ordered pair(s) ( x , y ) on the complex plane satisfying the relation (4-3 i) x2+(3+2 i) x y=4 y2-(x2/2)+(3 x y-2 y2) i is/are

Question

Possible ordered pair(s) ( x , y ) on the complex plane satisfying the relation (4-3 i) x2+(3+2 i) x y=4 y2-(x2/2)+(3 x y-2 y2) i is/are (A) (4, - 3) (B) (- 2, 2) (C) (6, 9) (D) (10, 15)

Tardigrade Admin · Accepted Answer

We have ((9 x2/2)+3 x y-4 y2)+(-3 x2+2 x y-3 x y+2 y2) i=0+0 i Hence 9 x2+6 x y-8 y2=0 ⇒ (3 x+4 y)(3 x-2 y)=0 ldots(1) and 3 x2+x y-2 y2=0 ⇒ (3 x-2 y)(x+y)=0 ldots .(2) From (1) and (2), we get 3 x=2 y ⇒ (C) and (D)

Q. Possible ordered pair(s) (x,y) on the complex plane satisfying the relation (4−3i)x2+(3+2i)xy=4y2−2x2​+(3xy−2y2)i is/are

(4, - 3)

(- 2, 2)

(6, 9)

(10, 15)

We have (29x2​+3xy−4y2)+(−3x2+2xy−3xy+2y2)i=0+0i Hence 9x2+6xy−8y2=0⇒(3x+4y)(3x−2y)=0…(1) and 3x2+xy−2y2=0⇒(3x−2y)(x+y)=0….(2) From (1) and (2), we get 3x=2y⇒(C) and (D)

Q. Possible ordered pair(s) $(x, y)$ on the complex plane satisfying the relation $(4 - 3 i) x^{2} + (3 + 2 i) x y = 4 y^{2} - \frac{x ^{2}}{2} + (3 x y - 2 y^{2}) i$ is/are