If z_1=2+3i ,z_2=4-5i and z_3 are are three points in the Argand plane such that 5z_1+ xz_2+ yz_3=0 (x ,y ∈R ) and z_3 is the midpoint of the segment joining the points z_1 and z_2 then x+y=

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Correct answer: A. (a) z_3= z_1+z_22=3-i Now, 5z_1+xz_2+yz_3=0 ⇒(10+4x+3y)+i(15-5x-y)=0 ⇒4x+3y=-10 … (i ) and15-5x-y=0 … … ( ii ) From equations (i) and (ii), we get x=5 ,y=-10 ∴x+y=5-10=-5

$If z_{1} = 2 + 3 i, z_{2} = 4 - 5 i and z_{3} are are three points in the Argand plane such that 5 z_{1} + xz_{2} + yz_{3} = 0 (x, y \in R) and z_{3} is the midpoint of the segment joining the points z_{1} and z_{2} then x + y =$

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