if (x+iy)(2-3i)=4+i then find (x,y)

 2x - 3ix + 2iy - 3i square y = 4 + i

(2x + 3y) + i( -3x + 2y) = 4  + i   ( becuz i square = -1)

comparing real nd imaginary parts we get..

3(2x + 3y = 4 ) 

2(-3x + 2y = 1)

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6x + 9y = 12

-6x + 6y = 2

now,

15y = 14

y = 14/15

now, put the value of y in eq... 1

2x + 3y = 4

2x + 3 * 14/15 = 4

2x + 14/5 = 4

2x = 4 - 14/5

2x = 20 - 14 / 5

2x = 6/5

x = 6/5 * 1/2

x = 3/5  ans..